A knowledgeable friend recently looked at a website I helped launch, and commented something like "very cool site, shame about the inline scripting in the source code".

I'm definitely in a position to remove the inline scripting where it occurs; I'm vaguely aware that it's "a bad thing". My question is: what are the real problems with inline scripting? Is there a significant performance issue, or is it mostly just a matter of good style? Can I justify immediate action on the inline scripting front to my superiors, when there are other things to work on that might have a more obvious impact on the site? If you pulled up to a website, and took a peek at the source code, what factors would lead you to say "hmm, professional work here", and what would cause you to recoil from an obviously amateurish job?

Okay, that question turned into multiple questions in the writing. But basically, inline scripting - what's the deal?