These are good points and I'm suitably chastened for not being sufficiently thorough in checking Toby Ord's claims,
I'm pleased to see that GiveWell is again investigating treating blindness: http://blog.givewell.org/2017/05/11/update-on-our-views-on-cataract-surgery/. In this very recent post, they say: "We believe there is evidence that cataract surgeries substantially improve vision. Very roughly, we estimate that the cost-effectiveness of cataract surgery is ~$1,000 per severe visual impairment reversed.[1]"
The footnote reads: "This estimate is on the higher end of the range we calculated, because it assumes additional costs due to demand generation activities, or identifying patients who would not otherwise have known about surgery. We use this figure because we expect that GiveWell is more likely to recommend an organization that can demonstrate, through its demand generation activities, that it is causing additional surgeries to happen. The $1,000 figure also reflects our sense that cost-effectiveness in general tends to worsen (become more expensive) as we spend more time building our model of any intervention. Finally, it is a round figure that communicates our uncertainty about this estimate overall. But it's reasonable to say that until they complete this investigation, which will be years rather than months, it may be better to avoid using the example of preventing or curing blindness." So the options seem to be either not using the example of blindness at all, or using this rough figure of $1000, with suitable disclaimers. It still leads to 40 cases of severe visual impairment reversed v. 1 case of providing a blind person with a guide dog.

The mention of the specific errors found in DCP2 estimates of de-worming efficacy, seem to be functioning here as guilt by association. I can't see any reason they should be extrapolated to all other calculations in different chapters of a >1000 page document. The figure from DCP2 for trachoma treatment directly references the primary source, so it's highly unlikely to be vulnerable to any spreadsheet errors.

The table Toby cites and you reference here (Table 50.1 from DCP2) says "trichiasis surgery". This means surgical treatment for a late stage of trachoma. Trichiasis is not synonymous with trachoma, but a late and severe complication of trachoma infection, by which stage eyelashes are causing corneal friction. It doesn't 'sometimes' lead to blindness, though that is true of trachoma infections when the whole spectrum is considered. Trichiasis frequently causes corneal damage leading to visual impairment and blindness. You are right to point out that not every person with trichiasis will develop blindness, and a "Number Needed to Treat" is needed to correct the estimate from $20 per case of blindness prevented. However we don't have good epidemiological data to say whether that number is 1, 2, 10 or more. Looking at the literature it's likely to be closer to 2 than 10. The uncertainty factor encoded in Peter Singer's use of $100 per person would allow for a number needed to treat of 5.

In this case the term "cure" is appropriate - as trichiasis is the condition being treated by surgery. At one point Toby's essay talks about curing blindness as well as curing trachoma. Strictly speaking trichiasis surgery is tertiary prevention (treatment of a condition which has already caused damage to prevent further damage.), but the error is not so egregious as to elicit the scorn of the hypothetical doctor you quote below. (Source: I am a medical doctor specialising in infectious diseases, I think the WHO fact sheet you link to is overly simplifying matters when it states "blindness caused by trachoma is irreversible").

[Edited to add DOI: I'm married to Toby Ord]

It's pretty much like you said in this comment and I completely agree with you and am putting it here because of how well I think you've driven home the point:

...I myself once mocked a co-worker for taking an effort to recycle when the same effort could do so much more impact for people in Africa. That's wrong in any case, but I was probably wrong in my reasoning too because of numbers.

Also, I'm afraid that some doctor will stand up during an EA presentation and say

You kids pretend to be visionaries, but in reality you don't have the slightest idea what you are talking about. Firstly, it's impossible to cure trachoma induced blindness. Secondly [...] You should go back to play in your sandboxes instead of preaching adults how to solve real world problems

Also, I'm afraid that the doctor might be partially right

Also, my experience has persistently been that the blindness vs trachoma example is quite off-putting in an "now this person who might have gotten into EA is going to avoid it" kind of way. So if we want more EAs, this example seems miserably inept at getting people into EA. I myself have stopped using the example in introductory EA talks altogether. I might be an outlier though and will start using it again if provided a good argument that it works well, but I suspect I'm not the only one that has seen better results introducing EAs by not bringing up this example at all. Now with all the uncertainty around it, it would seem that both emotions and numbers argue against the EA community using this example in introductory talks? Save it for the in-depth discussions that happen after an intro instead?

Here’s what I usually found most unfortunate about the comparison, but I don’t mean to compete with anyone who thinks that the math is more unfortunate or anything else.

1. The decision to sacrifice the well-being of one person for that of others (even many others) should be hard. If we want to be trusted (and the whole point of GiveWell is that people don’t have the time to double-check all research no matter how accessible it is – plus, even just following a link to GiveWell after watching a TED Talk requires that someone trusts us with their time), we need to signal clearly that we don’t make such decisions lightly. It is honest signaling too, since the whole point of EA is to put a whole lot more effort into the decision than usual. Many people I talk to are so “conscientious” about such decisions that they shy away from them completely (implicitly making very bad decisions). It’s probably impossible to show just how much effort and diligence has gone into such a difficult decision in just a short talk, so I rather focus on cases where I am, or each listener is, the one at whose detriment we make the prioritization decision, just like in the Child in the Pond case. Few people would no-platform me because they think it’s evil of me to ruin my own suit.
2. Sacrificing oneself, or rather some trivial luxury of oneself, also avoids the common objection why a discriminated against minority should have to pay when there are [insert all the commonly cited bad things like tax cuts for the most wealthy, military spending, inefficient health system, etc.]. It streamlines the communication a lot more.
3. The group at whose detriment we need to decide should never be a known, discriminated against minority in such examples, because these people are used to being discriminated against and their allies are used to seeing them being discriminated against, so when someone seems to be saying that they shouldn’t receive some form of assistance, they have just a huge prior for assuming that it’s just another discriminatory attack. I think their heuristic more or less fails in this case, but that is not to say that it’s not a very valid heuristic. I’ve been abroad in a country where pedestrian crosswalks are generally ignored by car drivers. I’m not going to just blinding walk onto the street there even if the driver of the only car coming toward me is actually one who would’ve stopped for me if I did. My heuristic fails in that case, but it generally keeps me safe.
4. Discriminated minority groups are super few, especially the ones the audience will be aware of. Some people may be able to come up with a dozen or so, some with several dozens. But in my actual prioritization decisions for the Your Siblings charity, I had to decide between groups of so fuzzy reference classes that there must be basically arbitrarily many of such groups. Street children vs. people at risk of malaria vs. farmed animals? Or street children in Kampala vs. people at risk of malaria in the southern DRC vs. chickens farmed for eggs in Spain? Or street children of the lost generation in the suburb’s of Kampala who were abducted for child sacrifice but freed by the police and delivered to the orphanage we’re cooperating with vs. …. You get the idea. If we’re unbiased, then what are the odds that we’ll draw a discriminated against group from the countless potential examples in this urn? This should heavily update a listener toward thinking that there’s some bias against the minority group at work here. Surely, the real explanation is something about salience on our minds or ease of communication and not about discrimination, but they’d have to know us very well to have so much trust in our intentions.
5. People with disability probably have distance “bias” at the same rates as anyone else, so they’ll perceive the blind person with the guide dog as in-group, the blind people suffering from cataracts in developing countries as completely neutral foreign group, and us as attacking them, making us the out-group. Such controversy is completely avoidable and highly dangerous, as Owen Cotton-Barratt describes in more detail in his paper on movement growth. Controversy breeds an opposition (and one that is not willing to engage in moral trade with us) that destroys option value particularly by depriving us of the highly promising option to draw on the democratic process to push for the most uncontroversial implications of effective altruism that we can find. Scott Alexander has written about it under the title “Toxoplasma of Rage.” I don’t think publicity is worth sacrificing the political power of EA for it, but that is just a great simplification of Owen Cotton-Barratt’s differentiated points on the topic.
6. Communication is by necessity cooperative. If we say something, however true it may be, and important members of the audience understand it as something false or something else entirely (that may not have propositional nature), then we failed to communicate. When this happens, we can’t just stamp our collective foot on the ground and be like, “But it’s true! Look at the numbers!” or “It’s your fault you didn’t understand me because you don’t know where I’m coming from!” That’s not the point of communication. We need to adapt our messaging or make sure that people at least don’t misunderstand us in dangerous ways.

(I feel like you may disagree on some of these points for similar reasons that The Point of View of the Universe seemed to me to argue for a non-naturalist type of moral realism while I “only” try to assume some form of non-cognitivist moral antirealism, maybe emotivism, which seems more parsimonious to me. Maybe you feel like or have good reasons to think that there is a true language (albeit in a non-naturalist sense) so that it makes sense to say “Yes, you misunderstood me, but what I said is true, because …,” while I’m unsure. I might say, “Yes, you misunderstood me, but what I meant was something you’d probably agree with. Let me try again.”)

Peter, even if a trachoma operation cost the same as training a guide dog, and didn't always prevent blindness, it would still be an excellent cost comparison because vision correction is vastly superior to having a dog.

If I try to steelman the argument, it comes out something like:

Some people, when they hear about the guide dog - tracheoma surgery contrast, will take the point to be that ameliorating a disability is intrinsically less valuable than preventing or curing an impairment. (In other words, that helping people live fulfilling lives while blind is necessarily a less worthy cause than "fixing" them.) Since this is not in fact the intended point, a comparison of more directly comparable interventions would be preferable, if available.