During the entire movie, Terry is constantly only hitting six keys over and over again when she types. Many times the number of keys she presses between pauses and lapses do not correspond with the sound or what appears on the screen.
When Terry and Jack are communicating with each other, a few times they refer to talking with the "consulate". They should have discussed talking to the "consul", which is a person, whereas the "consulate" is his office.
When Terry is giving the pregnant woman a hug in the beginning of the movie, there is nothing in the woman's hands. However, when they break the embrace she (the pregnant woman) is holding some fuzzy dice.
When Terry first contacts Van Meter, the clock on Terry's wall reads 12:15 (AM). We hear Van Meter say he can meet her in 20 minutes because he's scheduled to fly to Brussels at 3:00 AM; that would mean a meeting time of 12:35 AM. However, in the next shot, Terry is on the docks and states that it's 1:30 AM. That's over an hour later, and is not enough time (theoretically) for Van Meter to get to JFK for a 3:00 AM flight.
When Terry is scaling the roof at the British Consulate to get into the computer room, her belt is ripped off her gown. The belt and the tape recorder that was tucked into it, fall onto the sidewalk below. When Terry looks down, both her belt and the tape recorder are gone.
In the scene where Lady Sarah Billings stops by Terry's apartment with the contact information, she is wearing dark colored gloves. When she hands the envelope to Terry, the gloves are off, but as she leaves they are back on.
Terry Dolittle was interviewed at the police station after Terry (and Van Meter) were in the river. The cop stands up twice (different camera shots). In one shot he strikes the desk (and some papers) with his left hand. in the other, his hand is resting on the desk edge.
When Terry is using the phone booth to find Lady Sarah she is standing to the left of Cole's Restaurant (famous for French Dip Sandwiches). Two times during the phone booth scene she comments that she is in New York & she runs past Cole's again while escaping the NYPD later. Unfortunately, Cole's is located at 118 E. 6th St, Los Angeles, CA.
Lady Sara tells Terry that MI5 helped her get the exit contact for Jack. MI5 is concerned with Internal Security in Britain. Since Jack was out of the country, MI6 (external security) would be the agency establishing an exit contact.
When Terry is arrested, there are several glaring mistakes in police procedures, especially considering that she was a "woman with a gun." She is not handcuffed and the back window of the police cruiser is open.
When Terry gives Jack the set-up contact details, she tells him to meet him at five pm the next day. Come three pm the next day where Terry is, and after her race back to the bank to warn Jack, she finds him just leaving to meet the contact. Jack is in Russia which would be at least seven hours ahead of New York. This would mean that Jack would be long-gone by the time Terry even finds out his contact is a set up, and would already be dead.
When Terry's apartment was broken into and Marty comes to her door, you see her door with the broken, fully engaged chain locks hanging on the inside of her door. If her apartment was broken into when she was not home, the locks would not have been engaged and both ends would be undamaged during a break in. The same thing is again shown when Lady Sara shows at her door to provide an exit key for Jack and she tries to tuck it into the door.
When Mr. Van Meter is shot several times and presumably dead, he falls in the river, he surfaces next to Terry.
A gasp is seen and heard, and he blinks once. The position of his head also changes completely from one moment to the next.