OK. I can only speak from 6 months or so experience here, so I need feedback from the old timers.

What is the best, safest way to clean game cartridge contacts? Especially NES?

In my short experience, I've had nothing but success with Q-tips and rubbing alcohol, using this method:

Take a Q-tip, and some rubbing alcohol. Lightly wet one end and clean the game contacts. (Take care to not use enough alcohol to cause any 'runoff' into the cart - tilt cart if necessary) Dry the contacts with the dry end. Repeat until your Q-tips come out with no black residue.

I've read, in other places, claims that this is a BAD long term solution. If it is edumacate me, and tell me why. What method is better?

In my opinion, with the NES anyway, 40% of blink is caused by filthy carts, and 60% is caused by the crappy 72 pin design.

If this has been covered to death, my apologies to all.