2. Fact vs Fiction
Most of the facts of the case are presented in excruciating detail to be as accurate as possible. However, it follows closely the books written by Robert Graysmith who is often criticized for jumping to conclusions and making accusations without enough evidence. The books and the movie are both great, but should not be thought of as entirely factual.
3. Out the Window
I was disappointed with one section of the movie. The scene in the book when Zodiac tricks a young mother into accepting a ride and then threatens to killer her and her baby was one of the most frightening things I've ever read. It kept me up for a few nights, and I actually started sleeping with a baseball bat by my side. The scene in the movie definitely didn't have that level of tension built into it. Perhaps Fincher, like a lot of others, considered Kathleen Johns to be an unreliable witness.
You can look at most of the actual as well as unsubstantiated Zodiac letters online and try to figure some of the ciphers which have yet to be decoded.
5. Part One
The book and the movie both focus on only a few Zodiac suspects and really pretty clearly point to one in particular. In reality there are hundreds of possibilities. In fact Ted Kaczynski, the Unibomber was living in the Berkeley area during some of the Zodiac activity. It seems more like wild speculation than a legitimate theory, but it is pretty interesting. Unsolved Mysteries even did a piece about the connection, Part 1, Part 2, part 3.