I have sat multiple times in every section of the theatre, and the absolutely worst seats are in the rear mezzanine. There is just not enough elevation between rows. If you get someone tall in front of you, you might as well go home, because you are going to barely see the stage and frustration will rise every time the person in front of you moves at all.
I have sat in the balcony a number of times and have always found those seats to be very good even; the elevation between rows is good, and I have always felt -- more than any other second balcony theatre, bar none -- that they provide excellent sight lines. You are not going to see subtle nuances in a facial expression, but you certainly don't have an issue with The Prom.