Well, all these problems appear to be related to one thing, ActiveSync. By default, it attempts to connect every 10 minutes or so to synchronize the PDA. Unfortunately, it appears to do this even while it's not in the cradle, which of course, drains the battery and causes other strange side effects. And the option to change the sync frequency is greyed out, so you can't change it. And even if you kill the ActiveSync process, it'll keep restarting itself.
Unless you go into ActiveSync and add a server source. Just type in some meaningless IP numbers for the server. Once you create a server connection (you don't have to actually connect to it), the greyed out menu Schedule becomes available again. Just set everything to Manual, then you can delete the server connection, and ActiveSync will quit trying to reconnect all the time. You can then kill the ActiveSync process using the switcher bar or other task manager, and it will stay dead until you set the PDA in the cradle.
So far my PDA has been behaving itself for 4 hours, which is better than it's done since I installed the WM5 "upgrade". This still requires more testing, but hopefully it'll work until Dell releases an update (supposedly November 24th).