Movement

What is the camera attached to?

I feel confident that the big heavy coin case is stable, so I would blame the tripod or head. It's actually pretty hard (expensive) to get a tripod that works. Make sure everything is tightened down as much as possible, and spread the legs further apart if possible. Try tapping on the setup lightly in different places while looking at a live view to see where weakest points are. If the tripod itself is wobbling, you might get some improvement by putting the feet on bean-bags. If it's the head, you might only be able to improve by going to a better support, like a copy stand or microscope stand (or higher-end tripod and head).

It's also possible that the big pane of glass is acting like a drum and amplifying vibrations. The solution there is to set up the tripod on something else or on the floor.

Whats a wireless Mouse? I bet its one of them there new fangled things, will see if best buy or frys is having a sale.

Are you using mirror lock up? That is enough to blur an extreme close up image, - the mirror slapping up out of the way of the light path to the sensor), you might want to also try hanging some weight off the bottom of the center coloum of your tripod, adding weight there will pull the whole assembly down and prevent tripod shake.

I just borrowed my roommates carbon fiber tripod rig ($800) amazing how much more stable it is over my heavy duty aluminum Bogen model, and at 1/3 the weight.

One last thing to check the center column is tightened down, I've forgot that before and it will induce wiggle, slightly but perceptible.

OK Wireless mouse installed. Have to admit I like it but has not helped the issue much. Also suspended a roll of Ikes from the Center of the tripod.
Still getting a fair amount of shake. I don't want to increase the light too much more and shorten the exposure time I like the results with lower light levels and longer exposure times. But I think unless I can do something about the movement I am going to have to go this route.

If these dideas don't help, I'd say it's the tripod. I have a big heavy aluminum Bogen Manfrotto tripod that is solid, but after borrowing my roommates light weight carbon fibre tripod, I'm blown away by how solid and steady it is. Huge difference in long exposure shots over my 20lb Bogen and his is only about 4lbs. But then again it colst more than most people would want to pay around $675.00 with the head and QR system. Ouch expensive, but I'm sold and want one now, not just for coins, but for packing, I'd use a tripod a lot more if mine wasn't so dang heavy.