Loved every minute of it. Cried my eyes out, it was sad and poignant.
I wasn't looking for plot holes and the story doesn't really matter that much, it was a fitting goodbye.

I just had a couple of questions about the Master and apologies if it has already been discussed before,

why could he fly and why could he shoot energy from his hands?

Because his resurrection went wrong and all the time lord energy in his body was ripping him apart.