How much importance usually lies with how well the cake coordinates with the competition's theme? Especially if it's a vague theme... wouldn't be so bad if it was something specific.

Usually the 'rules' for the compition are stated, including how much value is given to what. It really depends on what the show people are looking for.
I would say it won't count that much. Not everyone makes a design that is specific for the theme of the show. Usually more is thought of the perfection of work, color coordination, neatness, etc.

It depends on the competition and what the rules say. For instance, in my state fair, representation of theme is one of the most important criteria. I entered my county fair a couple of years ago and there was no requirement for a theme, BUT they loved that I incorporated the fair's theme into my cake. In another show I enter each year, the extravagant cake category requires the representation of a theme and it's very important in the judging. The divisional categories in the same show aren't even judged on theme.