Do peer reviews go to just anyone, or do you need a certain amount of reputation to review suggested edits?
As edwinksl already pointed out, all users above 2000 reputation (sorry for stealing that I don't see the numbers anymore) can review edits.
So reviews are done by the community, or to better quote whats on the reviews page written:
Ask Ubuntu is moderated by you.
Help your fellow members learn to use the site and raise the quality of Q&A by:
- Evaluating new posts
- Voting to close or reopen questions
- Reviewing suggested edits