Yes, I've seen it bring up a banner for new tweets loaded when the app had been quit ages ago
A couple more I've seen recently - the window stack handling seems to be a little worse than the last version Daniel released, sometimes it gets confused and needs multiple 'back' clicks; the newer windows perhaps aren't tidying up the stack properly or something happens in between them appearing and being closed which confuses them.
Also when you use multiple accounts, if you switch a different account to be active when you're looking at one account's tweet page (whichever tab you're in), it doesn't update the home screen with the main stats on for the new account, and I'm not sure if it updates the tweets for the new account either.
I should probably file these on garage... (but bet I won't).