When I was in grad school doing research for my dissertation there was more than one time when I came across a great quote I wanted to use, read the original source, and found it didn't have that quote at all. At least twice I searched for that "quote" online and eventually found that it started life as a paraphrase of the work in question and the book I first read and taken it as a quote.

In more casual reading I will more often find someone making a grand claim with only a citation to support it and I want to make sure that the source actually makes a solid argument for that grand claim. So it might be something like "Charles Babbage predicted the internet" and I need to go see what he actually predicted to see what he actually said/wrote (I just made that example up)