During the tavern scene, Earl bangs his glass on the table and marches off to complain about the service. When he returns with a waiter in tow, the positions of the glasses/bottles on the table have changed, and there is also a second lantern on the table which was not there previously.
When Mae, Jerry, and Earl go out to to a club after the movie, the amount of beer in Mae's mug keeps changing between shots, as does the amount of foam in everyone's beer.
When Earl is trying to hand Jerry money to pay his father's bar tab, the condition of the bills and they way they are held in Earl's hand change between perspective shots.
During the second half of the film, numerous references are made to oppressive heat. The temperature in Monterey rarely reaches the upper 70s.
From Google: "In Monterey, the summers are short, comfortable, dry, and mostly clear and the winters are cold, wet, and partly cloudy. Over the course of the year, the temperature typically varies from 44°F to 68°F and is rarely below 37°F or above 77°F."
At the beach, Earl asks Mae, "Where did you get those blue, blue eyes?"
Barbara Stanwyck, in fact, had brown eyes.
During the tavern scene, Mae and Jerry watch the moon rise over the ocean. The film takes place in Monterey, California, which is on the West coast, where the moon rises over the hills and sets on the ocean.
When Peggy races Joe back from the beach to the pavilion where Earl is sitting, it is apparently one clean shot. However, Earl is clearly on a stage set (note the multiple shadows indicating illumination by stage lights, not the sun). Thus, when Peggy/Joe are running to Earl, the viewer (and Earl) are seeing a film of Peggy/Joe on a back-projected screen. It is when the actors emerge from behind the rock that Earl (and the viewer) are seeing live actors.
(at around 13 mins) When Mae walks past Joe in the Doyle house (Joe: "It's your life." Mae: "Yes, that's what's so funny. It's really mine."), a moving shadow of one of the crew can be seen on the floor at the bottom left of the screen.
(at around 10 mins) When Earl rewinds the roll of film, he uses a manual crank rewinder from reel to reel. One of the reels is wrong, because he is putting the outer film side on the inside of the new reel.
During the wedding reception, when Peggy (Marilyn Monroe) gets up on the table, Earl (Robert Ryan) mistakenly calls her "Mae".