When Finlay breaks the window with his gun, pieces of broken glass are left around the edges of the window frame. In subsequent shots, there is no broken glass in the window frame.
When Montgomery is first interviewed in the police office he recalls what happened in Samuel's flat in a standing position on the left of a seated Keeley. By the time his story finishes he is sitting where Keeley was sitting and Keeley is now seated where Montgomery was standing.
(At around 7 mins) There is a portrait of FDR. The film was set post-WWII, and Truman was president. However, FDR was a beloved president, so it believable that many portraits of him would continue to be exhibited after his passing.
When Mary Mitchell goes to see her husband in the balcony of the movie theater, as she crosses the row to him, she moves through the projection of the film being shown. A movie theater would never place a projection booth where audience members could cast shadows on the screen.
When Keeley is at the door talking to Floyd, just before Keeley and Bill Williams leave Floyd's room, the boom operator is reflected, perfectly framed, in the mirror to the left of the door behind Keeley in two shots for a total of about 17 seconds.
(At 21.05) The shadow of the camera and dolly is visible just to the right of the hotel door, behind the MP, as Bill Williams enters the hotel to meet Keeley in the coffee shop.