Interesting topic! My off-the-cuff quick answers (so probably wrong, but I'll start the ball rolling):
1. More bits imply greater resolution and dynamic range, meaning cleaner louder and quieter noise floor. I have personally found this more useful in the studio for recording and mixing than in the final cut, but have limited experience with hi-res output (e.g. BD).
2. Greater speed allows smoother filter roll-off to prevent in-band (audible) artifacts from steep filters. These artifacts include poor pulse response (ringing) and related phase shift in-band. Of course, higher rates come at a cost, usually in higher noise and distortion.
3. Trading distortion and noise for speed can thus be complex, involving not only the DAC core (actual converter) but amplifiers after and digital filters before. Optimizing competing parameters is non-trivial...
4. Because of those trades, it is typical to optimize the design for a given (target) sampling rate and bandwidth, and the compromises made among specifications may not be the ones you would have chosen.
5. Bear in mind that in many cases both the noise and distortion is well below the audible limit and/or masked by other factors, such as room acoustics and distortion in the speakers (which typically dwarfs all other distortion sources in a system).
I've no doubt left out a lot...
FWIWFM - Don