When Det. Tobin and his partner enter the cafeteria where the murder victim had worked, near the cash register, sitting at the counter, is a man with no hat, glasses, with a cup of coffee in front of him, eating something with a knife and fork. When we next see that counter seat, there's a man with a hat, a different suit, no glasses, eating ice cream out of a bowl.
The Jane Doe is supposed to have suffered a shotgun blast to the face, but when the detectives show the tattoo artist a photo of her taken in the morgue there is no damage visible.
In the early scenes of the Jane Doe being found and the police's initial evidence collection phase at the crime scene, the crime scene changes back and forth between a riverside park with Manhattan seen across the river and Central Park in Manhattan.
Corrigan refers to the Jane Doe as Tattoo Tillie before the ME informs him that she has a tattoo on her wrist.
When Dr. Maher meets Det. Tobin in her lab, she clearly cannot read without her glasses. But when they are at the Botanical Gardens and then at the police station, she reads everything quite easily without them.