When Caroline is making tamales with Oscar's family, at one point she is standing over the stove stirring. You can hear the food crackling in the hot metal pot, yet she is holding one hand on the handle without any gloves, and then bring that over to the preparation table holding the hot pot with two hands, also without any gloves.
Oscar is singing familiar Christmas carols to Caroline and a crowd. The chords on the guitar he is playing should have changed to different positions as the songs dictate, but his left hand stays in the exact same place. Because of that, the chord would always sound the same. You hear the guitar music dubbed in correctly however.
About 15 minutes in, a woman takes a bite of her food and exclaims: "Wow! These are the best pancakes I have ever tasted!" There is one problem with that: her plate had a very flat pancake, plain, with no syrup of any kind, and simply plain blueberries and strawberries on top. She was seen picking only fruit, so she didn't taste the pancake. Not only that, the pancake being plain, it is doubtful it could ever be "the best" she'd ever tasted.
There is at least one saguaro cactus pictured in the background near a bench when the female lead is looking out over a lake. This cactus is native to Arizona and is not found wild in New Mexico.
The "masa" (dough) for tamales is made using cornmeal, which comes from dried corn, not fresh/marinated corn (as implied in the film). The corn husks that the tamales are wrapped in is also dried (not green).
Caroline arrives on the Kettle Valley heritage railway.
This is a vintage railway in British Colombia, Canada. It is nowhere near New Mexico.