Sorry to keep spamming the boards with my questions, but I'm really excited to get my gallery up and running.

In regards to my first test gallery at:
http://www.scottjung.net/blog/zenphoto/test/

I noticed that a bunch of my photos spill into my now-empty sidebar.

I tried looking all over for the code for that sidebar, but I think it's considered part of the WordPress header, in which case I obviously don't want to mess it it.

Is there a quick way to fix this, e.g., limit the number of thumbnails per row or something like that?

If I were to make a comment on this(which apparently I am) it would be:
When working with wordpress and zen photo, remove the css links in zen photo and combine the contents of the zen photo css with the wordpress css. I spent many many hours trying to clean up css conflicts between the 2 and the best way I came up with was combining the 2 which solved most of my problems and made it worlds easier to troubleshoot using only 1 stylesheet.

This is a bit of a problem. Unfortunately, I can't require theme developers to use any specific CSS rule names. You just have to do as Chilifrei64 said and make sure the ones in your theme don't conflict.