Continuity mistake: Clarice Starling is interrupted during her training course, and her clothes are sweaty, with a stain that goes under the breast and the "FBI Academy" logo. She rushes back to the building, and her jersey dried sufficiently up to be clean all the way above the logo. Even more obviously, when she gets in the elevator the V patterned sweat stain goes all the way to the middle of her back, but when she is making her way through the corridors leading to Jack Crawford's office, again the stain has dried off considerably. (00:02:55)
Other mistake: When Clarice goes to Crawford's office, she sees on the board a newspaper article titled "Bill skins fifth", but the article is not about Buffalo Bill. It's about Hannibal Lecter (his capture, the charges against him and so on). Nowhere is Bill mentioned. (00:05:50)
Continuity mistake: Clarice is waiting for Jack Crawford in his office at the beginning of the movie. In the close-up of the newspapers clippings (but also in the wider shot before that) you can see that the rightmost article ("FBI links Skinning" etc) and the white paper sheet it rests on are tucked underneath the main clipping at the center. However when Crawford actually enters the office and sits at his desk, behind him the clippings have changed position; the leftmost one is now touching the central one (it was a couple inches apart earlier) and the rightmost one overlaps it. (00:05:50)
Factual error: Jack Crawford lists Clarice Starling's accomplishments saying that she has a double major in Psych (ology) and Criminology and graduated "magna." Clarice talking with the creepy Dr. Chilton establishes further that she graduated from UVA, where she also followed Crawford's seminar. Problem is, the University of Virginia did not offer a Criminology major in the 90s (does now, but began only in the 00s) and to this day it does not have Latin honors. (00:06:30)
Suggested correction: Some colleges/universities allow "self-designed" majors. If UVA offered enough Criminology courses at the time, it would be possible for Clarice to have this double major.
Continuity mistake: In the beginning when Starling is talking to Crawford he is sitting forward when he's talking about Lecter's cell. The very next scene when he gives Starling her ID he's leaning back with his leg folded. (00:07:30)
Continuity mistake: In the very beginning, when Crawford calls Clarice in to talk about interviewing Hannibal, his left shirt collar is over his vest. Two shots later, the same collar is under the vest. (00:07:50)
Continuity mistake: Agent Starling is hit by Miggs' produce, which left no trace on his hand, and despite landing on her hair and eyelashes leaves no trace on her face in the next shot, but suddenly some drips on her jacket in the last close-up - again gone when she hastes back to Hannibal. (00:19:00)
Continuity mistake: Jodie Foster has very blue eyes. When they flashback to her childhood, when she is crossing the lawn to greet her father, the girl playing the young Clarice has dark eyes. (00:20:10)
Suggested correction: Eye color also can change with age. This happens in 10 to 15 percent of the Caucasian population (people who generally have lighter eye colors).
Babies born with blue eyes can develop brown or darker eyes as melanin is produced. And while eye color can get lighter with age (older than Clarice usually), a child her age with brown eyes won't develop blue eyes. They could turn green maybe, but not the blue color seen.
I just rewatched the scene you were talking about and they're not blue eyes they're actually hazel and the adult Clarice could be wearing contact lenses.
Revealing mistake: When Clarice is at the archive, she sees two articles, one entitled "Baltimore Psychiatrist Receives Highest Honor" and "New horrors in 'Cannibal Trial'." The column beneath both titles to the right is exactly the same, and in the first article, that same column is repeated at the leftmost and rightmost columns and in the second, is repeated at the rightmost column. That same column is scattered on every article she sees. (00:21:35)
Continuity mistake: Clarice is looking through the archived articles. She turns the knob of the microfilm reader, then it cuts to a close-up; the pen she holds between her teeth did a 180° turn, as shown by the metal clip switching side. (00:21:40)
Continuity mistake: When Clarice tries to push up the blocked door of the self storage container she puts her gloves on her lap. In the next scene the gloves have disappeared. (00:24:15)
Continuity mistake: Clarice uses the car jack to lift the storage unit door. In close-up, the blue part of the jack is dimly lit, but the car lights in the wider shots cast a much stronger light on it. Moreover, when she operates it in the shot between the close-up and the one when she says it got stuck, there's a string dangling by the jack that was not there earlier. (00:24:15)
Continuity mistake: In her second visit to his cell, Clarice asks Hannibal Lecter "What did you mean by 'transformation', doctor?" When he answers the towel on the sink has shifted, even if slightly, to the left, it is suddenly wrinkled as opposed to being almost perfectly straight earlier. (00:30:35)
Other mistake: Clarice on the plane with Crawford is flipping through the report about the first victim (third found). Despite being a report on a victim of a case already thoroughly analyzed, it is lacking pretty much every detail about the victim other than the name and an incomplete address, and the data about the coroner in its second page point at Cleveland but with a California 408 area code (this page is realistically visible in detail only through slow motion, even if the relevant aspects - zip code and town name - can be spotted at normal speed). Finally, when Clarice turns page in the next shot to get to the photo part, the page is different. (00:36:15)
Audio problem: On the plane, Crawford is talking about the first victim. He's out of frame as he mentions that she was the only victim he took the trouble to weigh down. Except for a brief moment, when you can see his lips, not in sync with his voice. (00:36:35)
Continuity mistake: While travelling from the post mortem examination, Clarice is in the back seat speaking to her boss. In going back and forth in conversation, her hair changes from being curled up to being curled under, all in one swift change. This is a different style and not done as could be by running your fingers through your hair as the camera cut away. (00:37:45)
Continuity mistake: En route to the funeral home, Crawford praises Clarice's profile and asks her if she has any question. Behind Jodie Foster there are several cars and a pretty characteristic configuration of the wood and hill. Brief cut to Jack Crawford, and when the camera is back on Jodie Foster, the landscape behind her has changed completely. (00:38:05)
Continuity mistake: In the scene where Jack Crawford and Clarice are examining the dead body in Elk River, the substance they apply under their nostrils changes in shape and amount applied. (00:42:20 - 00:46:05)
Revealing mistake: During the autopsy at the funeral house, Agent Ray Terry is taking pictures, aided by the funeral home assistant, Lamar. The actress playing the dead body does a great job throughout the scene, but exactly when it's time to take the first picture you can see her blink right as Lamar's hands pass over her eyes. (00:44:35)
Revealing mistake: In the examination of the corpse at the funeral house, a bug is removed from the throat of the victim. The bug is lodged deeply into the throat of the girl, to the point that when they pull it out, air is released from the throat it obstructed. But if you look at the first shot when Agent Terry puts his tweezers in the girl's mouth, you can already spot by the molar the tip of the cocoon - the bug is not that big, if the agent had already pulled it by that much the gas release would have happened already. (00:45:15)