I need to get up on roof anyway, so what should I inspect while I'm up there?
On shingles, look for shingles that might be broken, cracked, or missing, that are curled (no longer flat), and any that have lost their stone coating. The last two are important; this is the first sign of an impending roof failure and that your entire roof will shortly need to be replaced. 

If you have rubber seals around your vent stacks (between the metal flashing and the stack itself, make sure that the rubber is still pliable. If it is not, it is time to replace either the flashing with a lead one, or replace the flashing and seal unit with a new one.

If you have roof turbines, make sure that they spin easily without noise. The bearings in these are sealed; they will need to be replaced if they do not spin easily. 

Look for nails that have popped up through the shingles, or loose nails on flashings. These need to be sealed with either an elastomeric roof sealer or "3 hour" silicone caulk. Don't try to pound them back in. 

If you have a chimney, make sure that the cap/spark arrestor is firmly attached and is not rusted out. 

Remember that water MUST be able to flow down and out of things, so if you seal anything, seal around the top sides. You cannot seal, for instance, a dormer window where the siding meets the roof deck.