Great watches that are really fun to wear. The lugs are really long and the watch feels bigger than 36mm when you are wearing it.
Good reference here:
https://andres55.home.xs4all.nl/frames/airman25years.htm
The crowns and the hack mechanism are the main issues. Hands also. Sometimes hands are replaced with period-incorrect hands or just the wrong hands altogether (the hands are very distinctive). Different versions have different seconds hands (lollipop vs straight). Sometimes they have the wrong crystal (some have magnifier some versions have no magnifier). Sometimes the date wheel has been replaced with a later version (some are all black, some red). Sometimes the case-backs have been swapped. There are a lot of different versions and sometimes parts get swapped.
I would not buy one if it didn't have the proper cross-hatched crown unless the price was really, really good and the watch is amazing otherwise. Those crowns can be really hard to find and you might have to troll eBay for months. If the hacking mechanism isn't working that's not great, but there is an excellent watchmaker in Nevada who can repair that (Jim Sadilek,
Vintage Glycine Airman Watches Repair Price List), but it can be expensive depending on what exactly is broken. If the lower clamp is missing its clamping piece (clamps the bezel to keep it from rotating), that's not great either since somebody will have to fabricate it for you. Jim can also do that, but again it can be expensive. The lower crown is not crosshatched. Don't let someone tell you that a particular version didn't have the hacking mechanism. If the hack isn't working, it's because it's broken. Pull out the crown and wait until the second hand gets to 12, it should stop. If it doesn't, the hack is broken.