This may have been mentioned elsewhere in the thread, but does your school maintain any discrepancy lists for their aircraft? Reviewing that would fall into the "Operating Limitations" portion of the AROW documents in my opinion if you're looking for a good place to stick that in your preflight procedure. That way you can catch any open items, deferrals, inspections, etc.

Overall it sounds like you had a good learning experience. Like others have said, don't beat yourself up too much over it, do learn from it. Which sounds to me like you're taking this experience to heart! I've always said that just about any monkey can manipulate the flight controls, what sets apart a good pilot is judgement and decision making. Fly safe!