When at the hospital, Amy goes to see Travis in his room...Amy is crying Travis' coat on her left arm. When she opens the door, the coat suddenly disappears, only to reappear when she hugs Travis.
The characters refer to using a radiocarbon date on a skeleton found in a house after a house fire. This technique would not be used to age the skeleton since anything newer than about 1950 would only be dated as modern and would not give an exact date. Radiocarbon dating is used to date older artifacts and bone and gives a range of a few hundred years. It is not accurate to within a year or two.
The American flag in the Chicago district attorney's office is hung backwards. The stars should always be in the upper left when hung against a wall, whether horizontally or vertically.
When Travis is in the FBI Chicago field office there is an American flag on the wall hung vertically with the blue field of stars to the upper right. This is not the proper way to display the American flag. The blue field is always be on the top and to the viewers left. Admittedly this arrangement would appear "backwards" to many. For most countries to go from horizontal position one would simply rotate the flag 90-degrees to the right, such as Canada where the movie was filmed. However this is the standard for displaying the American flag.
Amy mentions the body in the wall reminds her of Edgar Alan Poe's "Murders in the Rue Morgue". Travis asks if Poe wrote about bodies in a wall and Amy replies "in the chimney". Poe did write a story of a body hidden in a wall, "The Black Cat", and any professor of literature that specializes in mystery writers and stories would have known that.