I can sharpen knives and my wood chisels just fine. Scissors-not so much. I did find out that our local sewing store takes scissors in for sharpening. They were very reasonable too., about $3.50 a pair. They have a week turnaround so I'll be making a couple trips to get mine cleaned up.
Apparently hair cutting scissors are sharpened with a rounded bevel and it's recommended to only have them professionally sharpened. I would ask at a barber shop or salon where they get theirs sharpened.
Rodney