The first time we see Max play the piano (badly) he has very short / chewed finger nails. When playing the following day at his home, his nails have grown and are well manicured.
Penelope's lipstick changes in between where she walks into Max/John's apartment and when she comes out of his bathroom.
The film is set in an imaginary country, which freely mixes European and North American design, fashion, currency, automobiles, etc.
When Max jumps back in the doorway, the camera moves from his right lapel to the left. It is actually the reflection of him in the mirror, as noted by the buttons on his shirt jumping to the opposite side also.
(at around 50 minutes Amazon Prime time) A part of the mattress can be seen when Penelope's mother faints in the kitchen.
When Penelope comes out of the bathroom in Johnny's apartment, the handle on the outside of the bathroom door does not move, which it should when she turns the handle on the other side of the door.
In the shots of newspaper front pages, the same paragraph is repeated.
In the 1980s prologue with Jessica and Franklin Wilhern rushing to the hospital over the birth of Penelope, 2000s vehicles are visible in one driving shot.
The newspaper headline reads "Wilhern's in Hiding" whereas it should read "Wilherns" with no apostrophe.