Is Thanksgiving turkey bad for dogs?

Three dogs --- Turkey is totally their favorite food. They absolutely love it. But.....they all get diarrhea every Thanksgiving when they get turkey (chicken and other meats do not do this). I am going to cut back on the amount I give them - and try and give them only white meat - no dark meat or skin - to cut down on the fat. Hope this helps because they really love it - and I always have a lot left over. cjs