I notice that it is very hard to get the actual character of the track from seeing it on TV. Hard to perceive the elevation changes, hard to see the changes in camber and surface, and the abrupt changes in camera perspective can make it hard to grasp the flow of the track.
I also notice that I am amazed by how much the bikes slide around, and wiggle under hard braking, and how rough some riders can be on the controls while others are silky smooth.
When I watch videos (especially on-board videos) of amateur racers I am amazed by how many errors some riders make in races. Riders that are fast, judging by their laptimes, but make a lot of mistakes; it would seem surprising that they don't fall down more often - but then sometimes I find out they DO fall often.
It certainly seems possible to pick up some incorrect ideas or not-useful information, for example I sometimes hear announcers throw out some thoughtless comment or platitude that is really not applicable and could be confusing if you tried to really take it seriously. On the other hand, seems like you could learn a lot about preparation and race strategy, tire wear management, and race rules by watching races, by seeing what happens to riders that are late to the grid, or overwork their tires in the first part or a race, or choose the right or wrong tire compound, I find that stuff quite interesting.