2. This stood out a bit: when you break an equation into multiple lines, the equals sign comes in front of a new line. [Actually, in this particular question, the stackrels are upsetting the spacing. I do not know the solution to this. Perhaps I will ask JM or tb or robjohn later today.]
@Mattilda Oh, the difference is in the spacing between mod and the things surrounding it. For example, n a \bmod 1
looks better to me than n a \mod 1
.