If you have a quality fence and your saw is tuned properly, you won't have these issues. I've told you how to resolve all of your table saw woes, Collin.
At what point do you start valuing your time as much as your money?
Rex, if you're asking about the inside corner on top, you're trying to touch a square corner with a round bit and it will never reach! As mentioned, using a rasp and/or sanding block will be good options.
To strip old boards I just run them through the planer. I usually run rough stuff through on the right half of the blades, then finish out on the left.
Most woodworkers find this to be a horrifying offense. But, other than dulling the knives, it doesn't hurt the machine and I just consider that dull knives are the result of production.
I have taken the same approach with my 12" DeWalt planer (which has been in use since '98,) my 15" Jet planer, and now my 20" Jet planer with Shelix cutter head.
That old pine is really some gorgeous stuff too. That is a sad story!