A wounded Zombie finder, or: how to find the almost dead undead?
Not utterly wrong, but

q.PostTypeId = 1 


and

AND a.PostTypeId = 2


are superfluous. The only post types with a non-null value in ParentId are answers (see the Database schema documentation), and their values are the ids of questions, so the join already takes care of this.

I'd slightly misunderstood the objective of the query at first, because questions with answers with negative scores, like this one also appear on /unanswered. But you want to review the answers to see if they're worthy of an upvote. Then, you might as well drop the second column (MAX(a.Score) AS [Best answer score]) because you know it's going to be zero.