Most of the museum boats have had their screws removed to reduce corrosion problems with the hulls due to electrolysis from the bronze screws. When you put steel and bronze together in water -- especially salt water -- it sets up an electric current that slowly eats away the steel. Ships have zinc castings attached to the shafts to reduce this, as the zinc is less "noble" than steel and is eaten first. If you're not planning on going anywhere, the simplest solution to the problem is to just remove the screws.

There are some others that could probably move if you put the screws back, of course. I don't think any of the WWII boats could dive, since the Navy preferred to remove the batteries before turning them over. Cod, located in Cleveland, may be the most thorough restoration job at this point, and is the only museum boat that hasn't been modified in any way to get the tourists in and out. You still use the original vertical ladders. Judging from their site (http://www.usscod.org) she's been repainted in the standard gray and black pattern used during the War since I was there a year ago. (Horizontal surfaces are painted black, vertical surfaces are painted haze gray, creating an effective solution for hiding from both planes and ships.)

J.T. McDaniel