In my introduction, I mentioned "the civil rights movement in the 20th century," but then I talked about the French Revolution instead as an example. Do you think this will have a negative affect on my essay score?
Probably not. SAT essay graders understand that you're writing in a high-pressure timed situation and will overlook a few errors. As long as the rest of your essay was logically consistent, you should be fine.
The same thing goes for essays on the March 2016 (and later) SAT. If in your introduction you say that you'll discuss the author's use of anecdotal evidence, statistics, and vivid language, but end up discussing the author's use of anecdotes, statistics, and reasoning, you might give your essay's readers a moment of confusion. As long as your conclusion clearly relates back to what you've written in your essay and your examples are well explained, however, it's unlikely that your essay scores will be too hurt by this inconsistency - at most, your Writing score might suffer a little bit.