The men in white suits cut open part of the door but later on this hole disappears.
Mickey asks if they ever saw what happened to the Japanese when "we dropped Little Boy on Nagasaki". The Little Boy nuclear bomb was, in fact, dropped on Hiroshima on Aug 6, 1945. Nagasaki was hit with the Fat Man bomb 3 days later. However, it is plausible that the Mickey character gets the facts mixed up or fails to remember them properly in the stressful situation.
Near the end when Eva escapes the bunker (1h:56m:19s) the camera pans down and she is seen walking through a body of water. The left side reflection in the water clearly does not match the CGI background.
When trying the radio to call for help, they report their apartment building to be located on "The North-West corner of 29th and 5th". In reality however this is the exact location of a church (Marble Collegiate)