I was just wondering about what appears to be duct tape on the tail rotor.

Actually you can have tape on blades...I would not put any on the TR balde though. When I flew in Hawaii, we put blade tape on the leading edge of the main blades for erosion control...It needed to be changed every 50 hours or so. Occasionally, a peice of tape would get a "nick" in it and slowly start to peel away---we would land and pull it all off for the rest of the day.
I also flew a Hiller 12E many many years ago. It had old wooden blades that were balanced by wrapping duct tape on the outbourd edge of the main blades...One blades tape started coming off one day and destroyed lift.....I got it on the runway, (only just), and had insufficient power to hover, so slid all the way back to the ramp, where the electrics proceeded to catch fire....Never flew a Hiller 12 again.......