"Exceptional candidates from other areas may also be considered". What does this mean? I'm a fourth year mathematics postdoc and I am looking at tenure-track jobs this year. I see some jobs that have a targeted research area but often have a caveat sentence along the lines of "Exceptional candidates from other areas may also be considered." 

I am trying to decide if putting my file in there will cloud their applicant pool (since I am in a related field but not in the advertised discipline). What do caveat sentences like this mean? What does "exceptional candidate" mean? Should I apply?
Do not filter yourself out. You do not know what the hiring department wants (and they might not know/agree themselves). Just send your application in.

Do not worry about clouding application pool. The application pools are huge, but most applications are dismissed within a minute. As a member of a hiring committee, I prefer to spend an extra minute on one more non-competitive application than miss a chance to hire an excellent colleague who will work side-by-side with me for years.