Ending up with screen-inside-screen and having to figure out how to detach the inner one.
Having a program leave the terminal in some weird state when killed (either without echo, or in that weird alternate charset mode that can be fixed by _outputting_ ^O).
Not having job control at all (i.e. can't kill or suspend anything that I start in foreground) in some kinds of emergency shells (probably due to something like http://lists.busybox.net/pipermail/busybox/2002-June/006397.html).
Problems with terminals that are misconfigured so that control sequences are misinterpreted (most recently I had the issue when sshing to something that didn't understand `TERM=rxvt-unicode`).