I've read that corn gluten inhibits all germination even grass seed so you might want to switch tactics and purchase crab grass pre-imergence. Applying compost will help, but I'd wait until frost has past to do anything. Overseeding with grass seed will not germinate until the soil gets warmer.

Here is a link that might be useful: Propagating Perennials

The right time for pre-m is when the first blooms appear in anyone's garden in your neighborhood. Forsythia blooms are usually used as the trigger.

If you are on an organic program, then you can apply your choice of organic fertilizers at 10-20 pounds per 1,000 square feet any time within three weeks of YOUR "last frost" date. For me that was back in mid Feb.

For your thin areas, it makes a difference what your turf is. If you have KBG or bentgrass in it, then simply put some compost on top of the soil in the bare spots to try and prevent weeds from popping up. Those grasses are carpet forming types of grasses and will fill in the weak spots. If you don't have KBG or bent, then you probably have fescue. Fescue is a bunch grass which only spreads at glacially slow speeds. You would need to seed in those spots to fill with fescue. Unfortunately you will also get crabgrass sprouting at the same time. Oh and you cannot seed with anything and use a pre-m; the pre-m will suppress your seed along with the crabgrass. If you reseed the areas, just expose the soil, moisten it to an inch deep, scatter the seed, step on it to ensure good seed-to-soil contact, and dampen it. Don't cover it with anything. Water it like you did last summer for your new seed and you should be good to go.

Really your best bet for controlling crabgrass is to water deeply and infrequently and to mow at your mower's highest setting.

Next fall don't cut it short. The only reason to cut it short is IF you are reseeding. If you are not, there is never a reason to cut it short.

Here is a yearly maintenance schedule
Pay particular attention to the paragraphs on watering and mowing. If you want, just substitute your organic references.

dead grass and just soil underneath
I think you should investigate those dead areas. They would not be the result of failure of your seeding effort. Possibly grubs.

Whether to apply corn gluten or reseed the dead areas is up to you. If it were me, I would try to prevent crabgrass and wait until fall to reseed. You likely planted bluegrass which, as Dchall says, will fill in bare spots.

Tell what type grass you planted.

There was a typo in the post above. Here is the link.