Most job postings include an email (usually for the chair) to contact the committee's chair. I have so far never dared to use it for fear that i'd get sidelined for asking stupid questions. Things that I've wanted to ask in the past but haven't include:
Could I amend my application by adding document X (after deadline has passed)
Would you be interested in an applicant with a background in X and Y, having worked on Z (with CV attached)
Could I submit one more recommendation letter than the specified number?
Should the "Teaching statement" (or whatever they call it) include student evaluations (if they're not asked for anywhere else in the ad)?
Could asking such questions potentially hurt a candidate's chances?