When Max McLaughlin walks into the Displaced Persons bureau, the Colonel in an American uniform sitting at the front desk speaks English with a German accent.
The detective would have been an officer in a US Army Civil Affairs unit with a rank of at least Captain.
Karin is treated with penicillin for an infection. She takes pills. Penicillin for oral administration was not available till the early 1950's, as Penicillin V.
Moritz, a US Army sergeant, has a beard. The US Army, in 1946 and now, do not allow beards. Likewise, Max sports a 21st century scruff beard. The NYPD would not allow him to do that, and besides the vast majority of men in 1946 in the US and the world were clean shaven.
Major General Wright's uniform displays several modern decorations that did not exist during World War II, including the Army Service Ribbon, and the ribbons for the NATO Medal, and Iraq Campaign Medal.