I use a wet paper towel (or something similarly disposable) to wipe as much hair as I can, as soon as a limb is separated from the body. It's worth taking a few extra seconds (or minutes) to get all the hair off, using your fingers, wiping, burning or whatever BEFORE you bring it to the kitchen, if you section steaks and other cuts yourself, or before taking it to a meat preparation place. I thought it could wait and once I had a few steaks cut and a pile of stew pieces it went from one big piece of meat with a little stray hair to a bunch of pieces of meat with hair all over.pain.in.the.ass.
I also cut out any dark red or gelled/trauma-damaged blood on or (especially) through the meat. If its stinks (worse than the "good" meat) cut and toss, not worth the risk.
Hope it helps.