Mostly, a joke told by a person of a certain racial persuasion about their own race will go over OK if delivered well, but if told by someone of another race would flop with severe embarrassment (there are exceptions, but require a very talented comedian that can walk the line). It could be that Stewart tried to do just that, and it was taken the wrong way. I don't get the sense at all that he has any racial prejudices, from all of the interviews I've seen of him and his sincere behavior with fans of non-Caucasian persuasion. Plus, it looks like he had a very good friendship with Levar during the series.
Back to the OT... I saw some interview where Stewart had misgivings about how things were going after the first season. We all look at TNG with the success it achieved, but that was not a certainty early on. To me, it looks like midway through season 2, things started to get much better and then the changes for season 3 really cemented the success pattern. From what I saw, the cast became very enthusiastic for the series at that point, which probably showed in their performances (they got much better, IMHO).
Back to the OT... I saw some interview where Stewart had misgivings about how things were going after the first season. We all look at TNG with the success it achieved, but that was not a certainty early on. To me, it looks like midway through season 2, things started to get much better and then the changes for season 3 really cemented the success pattern. From what I saw, the cast became very enthusiastic for the series at that point, which probably showed in their performances (they got much better, IMHO).