I also spent part of the evening cleaning these new (to me) slide rules. It looks like the previous owner might have lubricated them with wax, which sounds like a good idea, and it does make it glide better... for a little while. Then gunk starts to build up and it begins stuttering and sticking.

I pulled the slide out and used isopropyl alcohol to clean the edges, then ran a plastic toothpick along the groves to scrape out the really stuck on bits. It already feels better.

Isopropyl is safe to use on a Pickett, since most models are made of metal coated with enamel paint. Never use any other solvents, or any kind of abrasives, since they may remove the paint and ruin it.

Once the old lubricant and dirt have been removed, you should probably relubricate the slide rule. Pickett recommended Vaseline, but I'm going to use dry Teflon lube. Most wood and bamboo slide rules should never be lubricated, and plastic usually doesn't require it.