Kurt Ullman wrote:
I am having my roof redone. Believing in "trust but verify", what are
some of the things I should be looking while they are here and for
awhile after they have left to make sure the job is being done properly.

All this has been said before.
Before the work is done:
Check recent clients for satisfaction.
Have a written contract.
Include unit prices for replacing sheathing & fascia.
Include specifications for replacement deck, roofing felt, shingles,
drip edge=s, and flashing.
Include - as noted by others - quality of flashing installation.
Include standards for clean-up both daily and at job end.
Include remediation for damaged shrubs and lawn.

When the job begins, keep a wrapper from the various materials and any
instructions that might be included. Check the manufacturer's web site
for installation instructions.
Don't allow installation over a wet deck.
TB