Paint defects and other cosmetic concerns certainly.
However, some may not be obvious during the time of the visit to the dealership and test ride, etc. Some defects/concerns may be only or more obvious during bright sunlight or artificial light; or hard to detect because of angle of view, rain, darkness, etc.
I had such a problem was that was difficult to detect during the bright sunlight when we inspected, test drove, and bought our Caliber - but obviously stood out under artificial light or when viewed from underneath looking upward at the car:
It's in the correction process now.
I have detected other defects during the initial inspection when purchasing other new vehicles. In every case where it was: an easily-correctable or minor problem, when the vehicle itself was just what I wanted, and it was something that did not prevent me from buying the vehicle otherwise - the sales and service staff requested that I take about a week of driving after the purchase to note ALL detected defects, concerns, and problems as a list and present them together in order to arrange a comprehensive visit or stay (with loaner vehicle) in order to correct it all at once.
I'm sure many replies will cover other things to inspect before driving the new Caliber off the dealer's lot. Ensuring all lights, seat and other adjustments, compartment doors and hinges, etc function properly initially come to mind.
Inspecting not just exterior but INTERIOR cosmetics for proper stitching, coverage, fit, appearance, etc are also frequently missed (I had a rear captain's chair on my last conversion van that had to be replaced because of a workmanship defect - the material was short and unattached on one side and left exposed, but was not visible until someone sat on it about 2 weeks after after I had bought it).
I'd say the bottom line is, no matter what, be sure to have the sales and service staff at the dealership be aware that you will make a list of any defects or concerns that you will likely or surely find after a short period of ownership, and make sure that they state that they will honor such a list and make the adjustments/repairs in a comprehensive appointment afterward.
However, as an exception, anything that could be disputable as whether it existed when you first bought the car versus subsequently should be reported immediately as soon as detected. Examples would be something that is more apparent to be DAMAGE-related (to validate any claim that it was obvious factory, delivery-transportation, or dealership damage - and minimize claims it happened after purchase).