Hm, never had any of these. The weirdest one I had, though was when, after messing with the batteries a lot, my Gen2 (not version 2, this is the one from 1997 or so) Tamagotchi went into HYPERSPEED mode. I swear, I'd look at the clock and about 2 and a half minutes would pass for every second. I couldn't even feed it as a baby because it would beep every few seconds before I could feed it. Since the menus exit after about 20 seconds of no button presses, I had to be really fast with feeding and checking stats, and I couldn't even play a game with it. Then when it dies and another egg came, everything went back to normal.
By messing with the batteries on the same gen2, I have feed and played with eggs and UFOs, and once had a teenage tama hatch into a baby. On Tamagotchi Angel, I got into games with a stick-figure-like character, but it would freeze and reset when I exited the game. Mostly though, the screen gets filled with garbled crap when I mess with the batteries like that.
