Personally didn't find anything wrong with the change. It sounds perfectly OK. Although, maybe the reason you find it odd is because it suddenly changes from A to Bb. If there was a transition from A - F7 - Bb, it probably wouldn't have sounded 'odd' as you put it.
However, the singer picks up the Bb chord absolutely fine... Nothing wrong with it either. With the kind of pitch-correction techniques available in modern recording studios, I doubt if an accomplished composer would let an off-key note into his song.
For me the song is quite good - could have been better, but no complaints.
You don't need long fingers to be a great solo piano player!