After I had my 68 blasted, I was very happy to see a clean body, but when you get in close there are a lot of seems and tight spots that still require some work. What is the best way to clean out those areas? Do I want to sand down areas like around the rear where the bumper was. There's a lot of adhesive type sealer material where body pieces are tach welded together. You would never see it when the bumper was attached but It gives me this feeling that I should clean up every nook and cranny.

Learning the hard way!

It depends on how well you want to detail your project. Remember, these cars were built on a moving assembly line and the name of the game was to make it look good from twenty feet away or cover it up. You have the opportunity to detail it in such a way that was never possible at the factory.

Strictly my opinion, but if you went through the hassle of blasting the body, take the old seam sealer out. At least on the exterior parts of the body. It is probably cracked and dry rotten.
Install new sealer and paint like new!

I agree with Tom. I have blasted my entire car and found out that beneath the cracked sealer there is usually rust. Don't forget the seams on you doors, hood and trunk lid. You can not get between the seams itself though, so you will never know you have removed it all.