After Walter's checkup, he puts his tie back on. At first, the skinny (back) end of the tie is longer than the wide (front) end. In the next shot, the front is properly longer than the back. When he goes to put his coat on, the back is longer than the front again.
When Bruce Baldwin comes to the press room late in the movie, an electric fan and small shelf on the wall to the left of the door both completely disappear. Both have been there in all previous scenes and both reappear after this scene.
The goof item below may give away important plot points.
Hildy wears black heels throughout the movie but when Earl Williams is hidden in the desk, she is pacing behind the table and is wearing white flats. The next time her feet are shown, she is wearing the black heels again.
After Earl fires the pistol, Hildy turns off the lights and pulls down the window shades in the press room. Then in the next scene the Hildy and Molly are talking to Earl while he is in the desk, the shades are up. The other reporters return to the press room and Hildy unlocks the door and lets them enter. One of the reporters immediately goes to the windows and raises the shades.