When Charles first meets "the Lady Eve Sidwich" at the party, his face goes from blank expression to shock twice - first with all characters, then in closeup.
When Jean is looking at Charles in the mirror, what she sees is the right way round instead of reversed. (This can be seen by looking at the cover of Charles' book.)
(at around 18 mins) When Charles and Jean are entering Charles' cabin on the ship, in the hallway Charles is using his right hand to open the cabin door, whose hinge is to his right. On the transition to an interior cabin shot, Charles' left hand is on the door knob, and the door's hinge is to his left.
When Charles and Jean are standing on the deck talking, the ambient, background sounds of people talking and birds singing can be heard running on a loop. The scene lasts several minutes, but the ambient sounds repeat every several seconds.
When the Lady Eve arrives at the party, having just arrived from England, someones asks haven't the boats stopped running (because of the war)? Oh, she came by submarine is the explanation. But, at the end of the movie, there they all are on board a ship again.
(at around 36 mins) When Charles and Colonel Harrington cut cards to play double or nothing, Charles loses the first hand and says. "That's $2000 I owe you." The Colonel replies, "For the moment", but his lips don't move.
When "Colonel" Harrington talks to Jean in her cabin the morning after Pike proposes, the shadow of a spotlight moves up and out of frame.
When Eve is presented by her Uncle at the party, she is referred to as "Lady Sidwich", but her real title is "the Lady Eve Sidwich".