After Graham finds out the video tapes are what links the victims the aircraft flying at dusk is the outline of a Falcon 2000. The film takes place sometime in the early '80s and the Falcon 2000 was not delivered until March of 1995.
When Lecter acquires Graham's address, the pulses heard in the handset do not match the ones he is tapping out. When you make a call this way the number of pulses you hear are matching with the tapped ones.
Actor Ralph Fiennes speaks with an impaired speech, mentioned as due to his character's Cleft Palette repair, but when we hear "flashbacks" to his childhood through voice over, the child voice actor portraying his character's younger self speaks without impediment.
When the lady at Hannibal's dinner party says, "Hannibal, confess. What is this divine-looking amuse-bouche?" she has a full plate of food in front of her. An amuse-bouche is a bite-sized morsel, or hors d'oeuvre, not enough to fill a plate.
When Dolarhyde is at The Brooklyn Museum, the woman who shows him the painting has eyeglasses hanging on a chain around her neck. After she says, "It's remarkable, isn't it? Two hundred years old... looks so fresh... so vivid", as Dolarhyde leans in for a closer look, she is now wearing the eyeglasses on her face.
When Dolarhyde cuts the bindings on the tabloid, he uses a bolster-lock stiletto with a bayonet style blade. In the next shot of the knife in his hand, when he is confronted by the newspaper seller, it's a swinguard lockback (no "picklock" or liner lock mechanism is visible at the bolster, making it a lockback) stiletto with a "standard" style blade.
When Will is teaching Molly to shoot at the farm, there is no visible recoil when she discharges the revolver. This would be practically impossible with a 357 or 44 in the hands of a novice. There is no flash either, just wisps of smoke. In fact, the gun shakes more while she's cycling the cylinder then when she discharges it. There are also no bullets in any of the chamber. Finally, neither are wearing safety goggles, which as a FBI field agents should be second nature when firing in a range-type setting.
At the end of the title sequence, following the prologue, the unseen killer rapidly flicks through the pages of his journal. Going through this sequence frame-by-frame reveals two identical pages - highly implausible in a scrapbook-style journal (The repeated page consists of one boxed article at the top, a picture at the bottom-left, and part of another article at the bottom right, the text selectively obliterated with a black marker pen).
The goof items below may give away important plot points.
Dolarhyde attempts to break through the bedroom door but stops just after damaging the door jamb. Later, after the shooting, Molly has to break the slats to get to her family, but the door jamb is intact.
On the beginning of the movie, immediately after Lecter stabbing Graham, the detective falls down, along with a basket full of arrows. Then he stabs Lecter with the arrows. When Lecter gets up, the camera shows Graham on the floor, but with no arrows or basket along his right side. On the next camera shot, the arrows are back in place.