Cdoc,
Yes, there can be problems with different kinds of brass aside from the primer pocket issue. I've run into at least one Eastern European case that was too thick at the neck. The original factory load used 0.450" bullets, and when I loaded a 0.452" it would not fall into my chamber. Europe uses some slightly different dimensions due mainly, I think to metric conversion tolerances and, occasionally, errors. You can find, for example, primer pockets that are about three tenths of a thousandth smaller than SAAMI minimum. The neck wall thickness was just an oddball issue I can't otherwise account for. I culled those cases, as there is no way it is worthwhile spending time outside neck turning .45 Auto brass. Jamming one into a chamber will raise pressure since it can't expand to release a bullet normally.
If you seat a bullet too long and it falls just a fraction short of letting the slide go 100% into battery, the gun may still fire OK, but the barrel, not being 100% locked up, will, in most designs, be tilted to throw the bullet high. That spoils accuracy.
Another common problem is the opposite of the first one I described: brass too thin at the neck. R-P's .45 Auto brass design is famous for this. In many dies it quickly work-hardens to become too springy to resize fully and you find bullets falling into the resized cases. This is also a sizing die issue. I had this problem consistently with my old Lyman carbide sizing die (late 70's or early 80's vintage; forget when I got it exactly). When I got my Dillon Square Deal for just my .45 Auto reloading, the problem ceased to be apparent. The Dillon dies seem to be tighter than normal—a form of "small base" die—which makes sense because a progressive commercial reloading operation, to be reliable, has to work with all brass. So changing to a Dillon sizing die is one solution to the R-P no-seats. However, I still cull R-P brass out of habit and because the fast work hardening means that even with a tighter die they get neck splits before other cases do.
Watch for short cases. Your cases change as you use them. .45 Auto operates at pressures too low to stick the case to the chamber wall during firing, so the cases back up to the breech where pressure makes them fatter and shorter in the tapered chamber. Resizing never quite returns them to full length and they end up losing about half a thousandth of an inch per load cycle. For this reason, if you start with cases at the tolerance average value of 0.893" length, after about 10 reloads they will be shorter than SAAMI minimum (0.888").
I followed some Winchester cases through 50 reloads once and by the end, the ones that hadn't been lost or split were all about .025" shorter than when I started tracking them as new, bulk brass. This does not make them unusable, but it does mean that you can't load them to headspace on the case mouth any longer. The rim is stopped by the extractor hook before the case mouths reach the end of the chamber, and with lead bullets that will deteriorate accuracy as they then tend to lean to the extractor side of the chamber and get swaged into the bore slightly off center. It opens groups about by 40% of original for me. It also means they need a different crimp die setting. To solve the accuracy issue with short cases, bullets have to be seated out to headspace on the bullet making contact with the throat of the bore (second from right, below). Fortunately, this practice not only corrects accuracy with lead bullets, but it minimizes leading.
The thing you want to do is segregate the brass by length to keep the crimp die setting correct, though I've not found this critical. With the taper crimp, if the cases are all within 0.005", that seems to be close enough for good accuracy.
If you mix the brass, you will get different crimp squeeze on the bullets due to differences in neck wall thickness. This seems to matter very little with some bullets and more with others. You will have to test them to see. Lead seems more touchy than jacketed, so I always seat it out to headspace on the bullet contact with the throat, as in the photo. That way the bullet is controlling start pressure rather than the crimp.
The .45 Auto is capable of great accuracy with an optimal load in a tuned gun. How much precision you really need or want to bother going for is an individual decision, of course. I kept at it for a time just to see where it could be taken. The same gun shot commercial cast lead to just under 1" at 25 yards.