Dr. Watson makes a comment about the stethoscope around Adam's neck. The ear pieces are hanging on Adam's left side. In the shot in the hallway, the stethoscope is now hanging with the ear pieces on his right side.
When Adam returns from obtaining blood from Dr. Watson, Eve has discovered the gun with the wooden bullet. Adam handles the doctor's bag as if it were empty rather than containing several cylinders of blood.
There is no way to get from the USA (Detroit or Chicago) to Spain (Madrid) only flying at night. The flight will take at least 8 hours and will cross 5 time-zones into the east towards sunrise. So night would take at least 13 hours.
The goof items below may give away important plot points.
Marlowe gives Eve and Adam the last of his "good stuff" - there is clearly very little left as they both tip the flask to drink the dregs. Cut to the couple in the street, building up the courage to go "a bit 15th century" on the lovers and they're taking decent drinks from the same flask and hardly lifting it - as if it's pretty full.
When Adam and Eve get up to "turn" the Tangiers lovers at the end of the film, Eve leaves the flask and her left-hand glove on the bench. The next cut is a two-shot with Eve wearing the left-hand glove, but not the right. Although this might be a continuity error, it could also be an ironic indication that the entire film to this point has been shot in reverse image, a sly dig at the notion that vampires are without a reflection.
When Marlowe dies, on the close-up shot of Eve as she raises her head from crying, Marlowe is quite obviously breathing. Not only is he dead, but according to conventional wisdom (even if not strictly stated in this version), vampires are not supposed to breathe even when animate.