The wiper motor in my '70 Duster runs very slowly in both low and high speed ranges. The high speed range is still slower than the low speed range on your average newer vehicle. Is this normal?

I was thinking about taking the wiper motor off of the car and disassembling it, cleaning it, re-greasing it, and installing it once again to see if that would help. Is that a good idea?

Also, if I were to take it apart, what kind of grease should I use?

Check your ground first. You have the classic sign of a bad ground. Run a wire from the wiper ground strap to battery neg. If wipers work correct clean the stud, nut and groubd strap onthe wiper motor. Also make sure you have a good body ground.