Continuity: When Clarice is opening the letter written to her by Hannibal, it is sealed with wax, and not glued down in any way. While she's reading it, Hannibal is shown licking an envelope.

Factual error: At the end of the film, Ray Liotta wouldn't be able to raise his eyebrows as the frontalis muscle had been divided.

Continuity: When Clarice is reading the letter from Hannibal, he does a voice over thing, however, what he says differs from what the letter says..specifically the "your good friend" before the signature, which Hannibal says but isn't in the letter.

Revealing: During the scene in which Krendler shows the fake Lecter postcard, look closely and you can read the line: "Sounds like him to me" although this line is part of Krendler's speech, and not part of the message itself. Forgetting your lines, Mr. Liotta?

Continuity: When Inspector Pazzi is in the phone booth calling the FBI at 1-212-555-0118, he doesn't dial the correct number. 

Continuity: In the scene when Rinaldo Pazzi (the Italian investigator later disembowelled by Hannibal) is searching on the internet, he types in a search "Hannibal Lecter reward", which returns one match.  The match contains the URL and a preview of the page, which gives the first sentence. That sentence however, incorrectly identifies the year of Hannibal's escape as being 1992; however when Rinaldo clicks on the link, the actual page lists the correct date as being 1990 in exactly the same sentence. [An extra comment - if you look closely, as soon as he clicks on the link the page opens, and we see a close-up of Lecter's face - just visible at the top right you can see the date 1992 mentioned. Then it cuts out to a wider shot of the whole page, and the date's magically changed to 1990].

Visible crew/equipment: Near the beginning of the film while Clarice is being interviewed, we can see a black T-shape during a shot of the floor. This is shown to be an actor's mark, as someone steps right into it a few shots later.