More specifically: I have a steel penny that's covered in black-ish crud that I was thinking of scrubbing off. Would a toothbrush and dish soap do the job? Or maybe toothpaste would be a good choice?
Sandpaper or steel wool works well. Seriously, cleaning is a no-no. But you're talking about a steel penny. You would probably spend more time and money on cleaning solution than what it's worth. Do what you want. Have fun with it. But if you have a coin of any value, leave it alone, or listen to one of the experts here. They know what they're talking about.
In nearly all cases, cleaning takes away from the value of a coin. In the case of a corroded steel penny, however, the value is already pretty low. However, a steel penny is made of zinc and cheap steel, so getting it wet might just lead to more corrosion.
Any added value a collector would put on a coin goes out in the rinse water. Improper cleaning as you describe would put it's value back to face. But then it's not worth more than that anyway. There are plenty of nice examples that have been properly cared for over the short life span of this issue.
never clean coins, apart from a dip in acetone to remove any traces of adhesive etc. the value of the coin will be dramatically lowered.
I picked up a can of acetone at the local hardware store. No luck yet in getting residue off any coin I have tried it with. Ultrasonic cleaners that use vibrations and soap to get stuff off surfaces are less problematic than most other methods. I have been submitting coins to NCS--they are the experts until they work on a coin they should have left alone. Their coppers spot removal service is a good deal. Worst cleaning methods: the finest steel wool--coin will be judged to be "whizzed" regardless. Polishing compound--again, even the finest product will have an abrasive effect. Various acid fluids, from vinegar and lemon juice all the way down to muriatic acid or Coke. Don't expect good results.
It's simply not worth the effort. You can buy these in nice, MS grade everywhere for just a few bucks.
Nope, sorry, you're not permitted to like it if it's covered in black-ish crud. Now, were it covered in brownish-crud...