The Lady Eve

In Preston Sturges's The Lady Eve (1941) Henry Fonda plays a rich boy scientist with either a really specific case of face-blindness or the intelligence of Buster Bluth, while Barbara Stanwyck plays a con-woman who can't seem to not fall in love with him. It's a classic romantic comedy, and in that the plot doesn't make a lick of sense upon any amount of scrutiny. It's got some funny bits though!