The only real issue I had with ST3 was the additional unexplained extensive battle damage on the starboard side and other untouched areas of the Enterprise. I think this was done by ILM as "artistic license"
Yeah, but readers of the comic saw all the extra adventures the ship had between ST II and III.
My most memorable aspect of ST III: I'd only just moved into a new flat and my friends congregated at my place to get dressed for the gala premiere. As we were nearing the cinema, I realised that I'd left the iron on.
It was very hard to sit through the volcanic destruction of the Genesis Planet knowing what might be happening back at my new flat.
Star Trek III: The Search for Spock premiere
by Therin of Andor
, on Flickr