I wouldn’t focus too much on any specific numbers. (But if you did want numbers, I think Messerschmitt’s numbers look about right.) Let me describe to you in more general terms the process (including potential spots for failure, since you asked), from my own research and experience. I am still a pilot applicant myself and have been in this process for quite a while. So I might as well try to help you (if you're coming back to this forum) and others in the mean time.
The ‘failing rate’ all depends on where you start counting the failures. There are people who want to be pilots who do not score high enough on the CFAT, which is the first thing you do after you submit your paperwork. Though if you are reasonably good at things like math, logic, problem solving, visualization, you should be alright. Good news is that you can prepare for this test to a certain extent. You cannot control the personality assessment part (TSD) that you fill out at the time of your CFAT, so don’t worry about that.
Next, if you don’t pass a reliability/reference/credit check, you may be disqualified or introduce a delay into your application until you resolve the issue. If you’ve kept a good character, been paying your bills, and haven’t robbed a bank some time in the past, you should be fine.
Next, a medical issue can be discovered during your medical or extended medical (additional tests that you do on your own), which can set you back or disqualify you. If you’re generally healthy, and don’t have anything out of the ordinary medically speaking, you are at good odds to go through. But you won’t know for sure until you do this.
Next, you may score low in your interview, which may put you at a disadvantage against other applicants. However, if you prepare well and have a solid resume, chances are you won’t have a problem with this. You can always improve your resume in the mean time by doing some leadership activities for example, etc.
The above steps (CFAT, TSD, reliability check, medical, interview) are more or less the standard steps, and you have a good chance of making it though them all, and even competitively. There is plenty of information on this forum on what you can do to prepare and help your chances to do well. If you have passed all these steps without trouble, you get scheduled for the aircrew selection test in Trenton.
Now this aircrew selection test is where you will be challenged, and I mean it. Historically, the average pass rate is about half, and that has been my experience when I did it. The dream will not die if you fail. You can do it up to 3 times, with a year wait in-between, if you wish. I would say this test is the toughest part of recruitment. Someone mentioned flying experience and its connection to this test. Some flying experience may have been beneficial back when this test was done in a flight simulator (CAPSS), but it has since been changed to a computerized test. You don’t need flight experience for it. But you will see some flight instruments in the test study guide, so… Take good note, and do with that information what you will!
If you pass aircrew selection, right away you go to Toronto for a more comprehensive medical exam and body measurements. Occasionally, people have been removed from pilot selection at this step, but again, you will not really know until you do it, so there’s no reason to worry about it. If you are exceptionally tall or have exceptionally long torso or legs, you can chat with the recruiter to get an idea if this may be a problem. (You need to fit properly in the cockpit of the training and operational aircraft.)
After you have done all that, your medical papers will be examined, and what’s known as your Air Factor will be sent to your recruiting centre within some time. You need an Air Factor of 1 to qualify for pilot. Once you are awarded this AF, you will be merit listed. At this point you officially enter the pool of candidates (the merit list) from whom the CAF selects applicants to award job offers. Chances are, this merit list will contain more candidates than job offers, and only top applicants will get selected. I believe your applicant score is composed from scores from your CFAT, TSD, interview, and aircrew selection test, so it’s important to do well on everything. But it still seems to be a mystery how exactly each part is weighted.
If you are merit listed, but not selected, not all is lost. You can wait and see if you make the next selection, or the next, and discuss your file with the recruiting centre in the mean time. Selections are not usually ongoing. They seem to happen only several times a year.
If you receive an offer, you go to BMOQ (basic training). Now I can’t say how tough it actually is because I haven’t done it, and I am going to assume very tough indeed, but presumably it will not be the toughest part of your career. It may help take comfort in the fact that thousands of officer candidates have taken and passed BMOQ.
Now you’re onto flight training, which will consist of Phase I, II, and III (among some other things). I have heard that the pass rate for Phase I can vary quite a bit. You can have the whole class pass or only say half. I have heard that this is the phase where you really get to find out if you are going to generally grasp flying or not. This is the phase with the highest fail rate, whatever that rate may be these days. Phase II will see a lot less people failing, and Phase III even less. From what I gather, the instructors are not out to get you, but help you to pass as much as they can.
If you are a direct entry officer (DEO), should you fail any of the flight phases, I believe you can either release or see if you can go into a different trade, depending on what you qualify for and what is available at the time (this is important for career planning, and should be double-checked with recruiter). If the military has paid for your education (e.g. ROTP entry plan), I am assuming it won’t be as easy to release, but I don’t really know anything about that as I am applying DEO.
While you should be success-driven, having some kind of Plan B is not a bad idea in my opinion when you’re applying for pilot. Have some other trades in mind that you think would suit you. As for vision, when I asked a flight surgeon what happens if vision deteriorates during service, she just said to get lasik, as if it was no big deal haha. As for age, I have been told multiple times that age is not a factor as long as you are meeting all standards. Just do your very best, always.
Finally, keep in mind this is quite a lengthy process. Your patience and motivation will be tested. The wait and especially the uncertainty are perhaps the toughest tests of all. From first application to BMOQ can take you under a year if you’re lucky, or more likely over a year. If will depend on how smoothly your process goes. For example, if you fail aircrew selection and wish to retry in one year, naturally you will extend your recruitment process by quite a bit. Also, some things become obsolete (e.g. your medical expired after one year), so if you are still in recruitment process, you will need to redo them. But don’t think like that. Full steam ahead and no regrets!
There are some good threads on this site on aircrew selection, pilot career progression, etc. Do some searching and you should find all this and other good info. I described the process here in one place so hopefully it helps new candidates like yourself to get started. (If I have made a mistake somewhere, someone feel free to correct me.) Good luck.
Mods, this thread should probably be merged with the ‘So You Want to Be A Pilot’ thread?