I would ask to see their configuration management procedures, including release procedures. It should be well documented and they should be able to tell you, down to a particular code file what revision went into a release.
Also look at their change management system. Have them walk you through a change. There should be identification of the change (the initial report), a review to assess the impact and to schedule the change, the changes implemented should be readily identifiable in the code and limited to what was authorized, and the changes themselves along with "near" areas should be regression tested (as dkusleika points out).
By the way, I don't know how well competence can be judged by a resume review. Some of the worst programmers I've known had the shiniest resumes. I'm not saying don't do that, just do so with eyes open.
Along those lines, look to how programmers are staying current.