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.
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.
In the Press Room Hildy yanks the private line telephone out and throws it in the corner. In the next scene the phone is connected again when she calls The Morning Post.
When Hildy is in Walter's office, a few lines before she throws her purse at him, his cigarette switches from his right hand to his left between shots.
When Hildy lights her cigarette in the restaurant, she takes it out of her mouth and waves out the match. There is a an instant cut to over her shoulder and the cigarette is in her mouth again.
During the lunch scene, at one point there is a fly very clearly walking all over the front of Cary Grant's suit.