Bill mentioned below that looking at these things comes across as making things hard. That's actually the opposite of being correct. If one comes across as many planes as I have, I would speculate they'l find some reasonable fraction of planes usable - smoothers and jack planes maybe a higher percentage than jointers. More than half of the jointers that aren't heavily worn will be somewhere around flat, and the rest of the fraction will have varying levels of low toe. I've seen (only once or twice in may be 25 metal jointers) very low toes nearing a hundredth. I'm guessing this is due to movement of castings (when it happens, I don't know, but certainly after grinding - presumably the castings season themselves in a short period of time and then stop - I've never lapped a plane and then had to correct it years later, not even infills).
If someone doesn't want to identify and define what problems are, that's fine. It's easy, just get a different plane, it's not mandatory to fix a plane that doesn't work well, nor is it that big of a deal to buy a couple of stanley planes (when materials for this hobby cost a mint, and they're never to be recovered again in value).
After flattening the #62 to dead nuts flat, and planing the edge of a board to get thin shavings, this is what the edge of the board looks like. This is just normal planing, planing through shavings (where I would normally get a slightly hollow edge - I can't actually tell if it's dead flat or a tiny tiny fraction hollow).
I didn't check this joint and replane or anything to get this, it's just what the plane does (ignore the oxidation on the left side of the straight edge, there's no gap).
Twist and concavity are the only real fatal flaws in planes - severe anything can be a problem. I've had exactly one modern stanley jointer that had little wear and had a significant amount of twist. I don't think it's worth worrying about. If in my giant sample size, I've seen one, then no big deal.
What makes hand tool woodworking easy is actually doing the right things to make it easy, and casting off (or fixing) tools that don't so that someone doesn't run around forums making it out like dogmatic routines have to be followed (e.g., spending 10 minutes with a table sawn board just to get a single edge joint, or dictating that the joint can't be had without match planing or fixtures - it's just not true).
When I post things that I've measured (not to measure, but due to problems) and give a heads up to what the issue may be, I'm not real jazzed about disproving suppositions - it's a waste of everyones' time and it confuses things even further. I'd be glad to address proof - in this case, "proof" could be gained only with an inaccurate straight edge. Testing what I say isn't hard - find a plane that's hollow in its length and try to make a rub joint or sprung joint. You can't do it. If you manage to bull or stand on a plane to get it to make one joint, then consider doing 20 on something important. The stuff about putting a plane on two boards and standing on it and getting it to bend more than a couple of thousandths is fine and good, but it's got nothing to do with using the plane.
Interestingly enough, the two planes that I found with bad problems - twist without much wear, and really low toe and high mouth - neither had much use. I wouldn't be surprised if they had little use because they were confusing to a user.
The millers falls jointer that I showed in a video on youtube (the seasick video) also had very little use, only a couple of thousandths hollow. I'm guessing lack of use is due to lack of success using. I've never had a significantly hollow plane with a lot of wear on it (a couple of thousandths hollow more more in shape of the plane (not mouth erosion, etc).