This example is not exactly censorship, but rather a strange choice of words of editing from TV to video:
In the late eighties, Sesame Street did a show where most of the human cast along with Big Bird go up on the roof to have a sing along. They are accompanied by Biff and Sully who repeatedly try to fix an antenna. As usual, these street segments are show in between other skits. At the very end, after a rendition of "What's The Name" Of That Song", the antenna that Biff and Sully had been working on collapses and the letter and number of the day are announced among closing credits. Well, these street scenes were adapted to a Sesame video called "Sing Along". At the very end of this video, the letter and number announcement would obviously make so sense since it was all street scenes, so they dub over the very last lines with a voice saying to Biff, "You call yourself a repairman?" Biff replies, "No, a Republican. I call myself a Republican." Didn't really make much more sense than the closing credits would have. I guess it must have been an inside joke. I couldn't believe it when I first saw it and had to rewind it to make sure I heard right.
BTW, this is a very good video that I highly recommend because it was a later showed that still had the essence of Sesame Street well defined.