This is the basic check I'd do and I could be wrong... It should only take a couple minutes.
Barrel feed ramps are clean and aligned with the upper receiver ( ie. if the upper has feed ramps milled into it) and the lugs are in good order.
Check gas block to make sure it isn't loose (if possible).
Check BCG - Is the carrier properly staked or nicely tighten and not loose, lugs on the bolt are clean and not overly worn, extractor is in good condition, gas rings are in good order (easily and cheaply replaced if needed).
Cycle the bolt with the charging handle. Does the bolt lock/unlock up nice and cleanly?
Basic function check - check the safety and make sure it functions normally, Check the trigger and make sure it functions normally ie hammer releases cleanly BUT guide the hammer down softly if the upper is removed. Just do not pull the trigger and let the hammer fall with the upper receiver/BCG removed to avoid damage to the lower receiver.
If possible, sight down along the top of the upper receiver and see if there is any misalignment of the front rail/handguard and upper receiver.
With the upper removed, hold it it upside down and see if the receiver shows any signs of warping esp if the owner has done any work on the rifle. This could be a result of not using vise blocks etc while installing the barrel nut etc.
Check to see if a magazine locks into the magwell and releases with the mag release.
Check to see if the BCG can be locked back with the bolt catch.
With a piston AR, check for carrier tilt wear by the buffer tube area.