For me, one of the unexplained quirks was how "mysterious time lord woman" could appear to Wilf if she is trapped in the time bubble, whoever she was supposed to be.
I had always detested Grant's ham-fisted modifying of The Master into a looney who can't get the sound of the drums out of his head. He should have been Moriarty but ended up as Herman Munster. I'm not sure how the ret-conning of the drumbeat being a plot by the time lords to get out of the time bubble worked as a story, because it raises too many questions about going back in the timeline etc. etc.
Regarding good bits, I'm sure that in Ep1 Wilf said something which was an homage to Bernard Cribbins appearance in the first Dr Who movie all those years ago. I didn't write it down though, and can't remember what it was!