Continuity mistake: The original scene where Leon is being interrogated is different to the recording of the scene that Deckard watches as he is driving. Even what Leon says is different, in the original scene I think he says "Let me tell you about my mother" but in the recorded playback he says "I'll tell you about my mother", and the line is delivered differently.
Other mistake: When Rachel shoots Leon through the head, you can see an exit wound on his forehead. When we see him from behind, there is no entry wound or even a sign of any injury on the back of his head.
Other mistake: When Joanna Cassidy hits Harrison in the neck with the side of her hand, Harrison doesn't react immediately as he should; he reacts, falling backwards, a few seconds after he is hit.
Other mistake: When Deckard is waiting for a seat at the Chinese restaurant, he is reading a newspaper, presumably the day's edition. On it, the main headline reads, "FARMING THE C...MOON AND...WORLD..." Later in the movie, when Deckard is investigating Leon's room at the Yukon, he searches a drawer lined with a newspaper page, all crumpled and having presumably been there for quite a while, stained with some fluorescent oil or such, but he briefly flips it over and it has the exact same headline.
Other mistake: When Deckard puts a photo into a machine that rests on top of a monitor, he then speaks where he wants the camera to go, zoom in, go out, up or down or across, etc. In one instance, he doesn't speak, but the machine works on its own.
Other mistake: The snake scale changes size and shape each time it's seen, it begins as a large hexagonal shape bigger than Deckard's finger tip when he first finds it, it's later seen as a very small triangular shape in the sample bag and it ends up as a guitar plectrum shaped object when he hands it to the street merchant for identification.
Continuity mistake: At Sebastian's place, when Roy kisses Pris on the nose, the powder covering her face and her nose transfers from Pris to Roy, so now Pris's nose is void of powder, but a few seconds later, the powder returns.
Continuity mistake: After Rachael shoots Leon when she and Deckard are in his apartment Deckard suddenly changes from his trench coat into a jacket.
Revealing mistake: When Dekkar retires the snake lady a spinner hovers overhead telling people to move on. At the back of the spinner you can see the cable that it's suspended from.
Continuity mistake: When Zhora collapses after being shot by Deckard, her legs are spread apart, but when Deckard approaches seconds later, her legs are suddenly together.
Continuity mistake: When Pris is fighting Deckard in the apartment, in some shots she is wearing pantyhose, but in other shots her legs are bare.
Factual error: When Leon gets shot in the head, Deckard is untouched by any blood, brains etc despite being directly in front of him - he should be covered in something from the head wound.
Suggested correction: From a human, yes. Leon isn't a human. We don't know anything about replicant anatomy. For all we know, they might not have any blood, and their brains might not even be in their skulls.
Continuity mistake: When Deckard shoots Zhora and she crashes through the window dead, her hands are above her head, but when Deckard walks up to her body her hands are now halfway up her body.
Revealing mistake: There are at least two rain related problems in the city exterior shots: it's noticeably misaligned when Rick and Gaff are outside Leon's apartment building (towards the right it falls straight down, yet towards the left it falls at an angle). The second is when Gaff encounters Rick and the now dead Baty on the hotel roof; despite previous shots showing no awning or any type of cover above said roof, Gaff is visibly dry and actually standing in front of the rainfall, only getting wet when he steps into the background.