The visor Murphy's wearing changes between camera angles from level to cocked at a steep angle, making it obvious some scenes were either shot out of order or had to be re-done.
At approximately 69 minutes, Hildy types furiously at a typewriter, however, with his right hand he only uses his index finger and pushes the same key over and over again.
(At 9:10) In the early scene in the Post newspaper office, as the camera tracks Walter Burns moving through the office, just before he exits through the door a crew member's back is visible pushing the camera along.