I won't bother with the plot, what there is of it is covered elsewhere, but I would make a correction in that protagonist Bob Mitchell is in the RAF not the British Army.
Sadly Bonar Colleano gives a decidedly stilted performance as Mitchell, but there are interesting appearances from some interesting actors: Eva Bartok, Gina Lollobrigida, stalwart Brit Geoffrey Sumner as the Wingco, Marcello Mastroiani and a cameo from Terence Alexander as a hotel receptionist.
As Mitchell travels from city to city, almost every meeting leads to a silly misunderstanding, all of which could be avoided if he just starts out by saying he has amnesia.
The movie does provide a glimpse of post-war Europe and shines a dim light on the plight of stateless refugees, but it's no Third Man.