I listen to a fair amount of NPR, or used to listen to a fair amount of NPR. One thing I really do not like is the current trend to increase the amount of ambient noise that runs with the material -- often noise that seems artificially added. When I'm driving, I do not need an extra, moving, crystal clear siren noise. Let the studio broadcast just be silent in the background.
Even worse is the growing trend of using ring tone "music" interlaced with broadcasts, as a sub-theme in theme music and in advertisements. Like a borderline personality disorder, the "music" cries out for attention, setting off people checking to see if a cell phone is ringing. While it calls for attention, it also seems to generate revulsion. Advertisements with those sub-themes are the ones most likely to trigger a changed channel rather than being patiently listened to/ignored until more news or music comes on.
Shows that use them are why I've given up on NPR and on radio in general.
I know, on the scale of things that are annoying or dislikable, what I've mentioned is pretty trivial, but it probably annoys me more than anything else I deal with. What out there annoys you?