When Booth grabs Laura to stop her dancing, her flapper beads end up hanging from her neck in two long strands, but later are shown intact.
When Booth first appears in 1927, "The Great Seed" movie poster facing the street has the sign "1927's big hit!" slanted down to the right and covering up the name "Booth." The different poster behind it has the "1927's big hit!" horizontal and "acclaim it" instead of Booth's name. When Booth runs back to the theatre from the speakeasy the posters are swapped. Then when Booth examines the poster up close it switches back.
The papers in Laura's hands change position while she in fanning air with them. Laura first grabs the papers as the camera shows three characters Booth, Laura and Barney, and the Dark Stripes on the papers are facing the camera. The next camera angle only shows Booth and Laura as she is still fanning air, but the papers are in her hands differently with the Dark Stripes now facing the new camera position.
Booth is standing at the window watching his wife frolic by the pool in a bathing suit but when he dresses he wears a coat, an overcoat and a thick scarf.
Templeton's last name appears to be misspelled on one of the "Great Seed" posters at the Savoy. It's a bit out of frame at the top, but it looks like the name is spelled "Templetoil". The last letter is definitely not an N - it looks like an L.
The woman---Pippa Scott, whom Templeton meets, dining at the restaurant---has thick eyebrows, giving away that she's an actress and actually in 1960, and not in the 1927 era that he's supposed to be in. (In the 1920s, women sported shaved, painted-on eyebrows, not gorgeous Elizabeth Taylor-like thick ones.) This distracts from "movie magic" as---the moment she is seen---it was very obvious that something was off, to be the Roaring Twenties.