I'm sure that's not the intention, but as a blog posting on Better Nation pointed out today, Scotland will probably have to join Schengen at some point post-independence, simply because England will be seen as the continuation of the UK, so Scotland will be treated as a new EU member, and they generally don't get many opt-outs (which will also mean that Scotland will eventually need to join the Euro).
Personally I'd be delighted if Scotland joined Schengen, given that we tend to travel much more often to Schengen countries (such as Denmark, Germany, France and Italy) than to England. Who knows, it might even convince the English to join, too.
Writing this blog posting, I was a bit surprised that I couldn't find a realistic mock-up of what Scottish passports will look post-independence, given that the layout of EU passports is heavily regulated.
It didn't take me long to make one myself in the Gimp, though. I made the assumption that it'll be the lion rampant that will be on the front page, although it might of course be some other emblem.