Continuity mistake: While waiting in the rain for his food, the chef across the street calls Deckard to come over. Deckard folds his newspaper and puts it over his head to shield himself from the rain. The paper is folded messily and the crease side is in his hand. When he gets to the other side of the street, the fold is suddenly much cleaner and neat, and the crease side is on the outside, no longer in his hand. (00:09:00)Quantom X
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.
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.
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 and Bryant are viewing the interview tape showing Leon's interview at the Tyrell Corp they are shown Leon's replicant statistics. The tape shows Leon's model number: N6MAC41717. This designates Leon as a: Nexus 6, Male, Physical Level: A, Mental Level: B, and an incept date of: April 17, 2017. The incept date shown under his model number is: 10 April, 2017. As Deckard and Bryant continue to watch the tape they see the other replicants: Roy, Zhora and Pris with their individual statistics showing a matching model number to their incept dates. (00:14:50)
Continuity mistake: When Deckard is snooping about in Zhora's dressing room asking questions. We see her putting on high heel mid-calf boots (just under her shin pads). Watch the chase sequence soon after. Especially when she gets shot and is on the ground picking herself up, you can see she is wearing what looks like black trainers. (00:52:10 - 00:55:40)lazarus1968
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.