The copyright issues will make your head explode. To be precise, there are copyrights in all of the songs (the compositions themselves), and all of the performances of those compositions, usually held by different people, plus a copyright in Tommy's breaks, and, finally, maybe a "compilation copyright" in how it was all assembled.
On the air, the first is covered by a blanket music license and the second is exempt (but not on streaming). The third and fourth are not problems, because they are owned by the station or the DJ.
Technically, posting an aircheck on the web violates all four copyright interests, unless it falls within "fair use" (for critical, commentary or other educational purposes, which it probably doesn't), but fortunately, no one seems to care a whole lot.
The question is best left unasked. >boom< (sound of head exploding).
Bill