Ive shot ammo from the 30's and 40's without issue. Ive shot stuff from the 70's and 80's that had problems. I think how its stored and kept has probably more bearing on it, than anything else. From what Ive read, according to the US military, arctic is good, heat is bad.
Back in the 90's, I bought a bunch of 70's era Malaysian 5.56 for cheap. Im currently finishing up the last of it, and Im now getting a lot of split necks in the cases. Never an issue up til now.
Ive also been having some issues lately with some old reloads I inherited that were loaded back in the late 80's, early 90's, that up until the past few years had been fine. I started to get splits in their necks as well, and in some cases, complete separations where the neck meets the shoulder.
When I first noted the problem, I pulled them down, loaded both the powder and bullets back into once fired cases, and all seemed well. I fired about 30 rounds of them, without any sign of a problem.
That box (and a few others) got misplaced during some rearranging, until a week or so ago, when I found them again. I figured Id burn them up now, as they are the oldest in the queue. First round out of that box that had the rounds 30 fired in it, had a split neck. A little lateral pressure on the bullet, and it popped right out. I start looking closer, and about 2 of 3 all have split necks. I get to checking on the other boxes, same thing.
From what I can tell, from a quick search online, its a degrading powder issue, and when the powder degrades, it releases an acidic gas, that builds pressure in the case and attacks the brass, at points of tension.
This seems to be whats happening in my case, and the fact that the once fired brass I loaded using the "old" powder, are the only ones that are having the issue, the same lot of cases I loaded with fresh powder, are not.
A member here who goes by "slamfire", has a lot of good info on this, if you do a quick search.
I would say if the ammo was kept in cool, dry conditions, and looks good, its probably fine. Just watch keep an eye on things as youre shooting.
Another issue with some of the older stuff, can be corrosive primers, which if you dont properly clean the gun (basically hot soapy water or old GI bore cleaner), you can have some nasty problems. Most of that stuff is pre mid 50's or so, but I have had some foreign surplus 9mm from the 60's and 70's that was pretty nasty.