Amiga 3000 with jerky mouse and icons switching to monochrome green

[matt3k]

Welcome to the 3000 club, it is a great box!

Definitely remove the battery and replace with a more reliable coin type.  I like the ones on Ebay the most.  

I would also recommend you replace the PALS with a good set of GALS, this is the only real failure area that I have seen with the box.  If you plan on using the zorro bus extensively pickup a Buster 11.

If your bored sometime checkout:
http://www.amibay.com/showthread.php?59870-Amiga-3000-buyers-guide-myth-buster-and-Refit&highlight=mythbuster

As far as the green icons, I would try a different video out if you have a compatible monitor.  Try reseating and cleaning amber.

Good luck!