Ugg... lots of misinformation here.
First off, unless it's a really old mouse, or the magnet is like a 1 tesla magnet, the mouse is likely to be unaffected. If it's a ball mouse, and it's a really strong magnet, it might cause some funkiness and/or the ball core might become magnetically charged... however I doubt you'd notice much.
The "brains" of the mouse would not be scrambled, unless, as I said, it was a really strong field (Even then, it would have to be ridiculously strong. You won't find magnets that strong short of wrecking yards and MRI machines).
Aluminum probably wouldn't do much as far as making an impromptu faraday cage, either. However, a cheap solution to a faraday cage would be to enclose the whole contraption in a chicken wire box. It would be crude and only moderately effective, but it would probably protect the monitor if it was elevated high enough.
Alternately, if you wanted to shell out a few more dollars, a fine mesh of copper wire would be spectacular, and would bring your magnetic field down to levels that are probably below the ambient fields you'll find in your house. None of this would be Tempest level shielding, but I seriously doubt anyone needs that for a MAME machine, unless you want to keep the Feds from knowing your playing pirated ROMs
