is it possible to visit/climb a minaret in Istanbul. There was a travel program that showed a guide doing so?
You can go into mosques, but I am not aware of any minaret that one could climb. I did not look, and this is a BIG maybe, but possibly at the Hagia Sofia it could be arranged since it is no longer a functioning mosque. Frankly, there is so much to see and do, I would not be overly concerned with finding one.
I'm betting not, but if you just want to get up high, try the Galata Tower.