Captain Davison's Army uniform does not carry any branch insignia.
The credits list the name of the professor character as Donald Mason but his wife and student girlfriend call him Bob. In his closing narration, Hitchcock refers to him as Don Mason.
At 22:10, when Mrs. Davidson brings her daughter out to the rear porch, she is holding a doll. When the camera shot changes, she's holding the real baby again.
The detective postulates that Claudia must have let her murderer into the house since there was no sign of a break-in; therefore the killer must have been someone she knew like a fellow student or a boyfriend. This overlooks the fact that she was babysitting at somebody else's house, so the owners of the house could have let themselves in.