Answers

I'd expect that you have a warranty longer than just 30 days. Probably at least 1 year, right? I'll base my answer on that premise.

In the first 30 days, you should look for things that are incomplete or not installed to the Standards Manual referenced in your contract. (My contract references the Residential Construction Quality Standards of the Wisconsin Builders Association.) If there were things promised in written or verbal contracts, change orders, etc that are not done.

Over the course of a full year, the lumber will fully dry out and the house will have gone through its seasonal shrinkage and expansion due to humidity & temperature changes. You should expect your contractor to repair screw pops and drywall seams one time in your warranty period. If you notice areas of trim that weren't puttied, expect them to touch it up then.

Any other things you can think of that you have questions about?

After 30 days most likely areas that might have issues are any fixtures or appliances- mostly they have an issue right away or are good for many years! Also, check under your sinks to make sure that the use of the sinks and faucets hasn't allowed any of the fittings to come loose. We use brass fittings and traps, but many contractors have moved to plastic which can become loose with initial use. Another thing we find occasionally is that 3/4/5 way switches might not have been wired properly, which sometimes only becomes apparent when someone starts living in the home. If you have a home control system, that can be something that might need to be tweaked or adjusted for your use. Using everything, making sure that everything works, those things are key in the first 30 days- Good luck!