When Nick and Billy are about to board the bus to Reno, they both trip and fall into puddles of mud and water. Their clothes get filthy, but the next shot of them on the bus, their clothes are clean.
With the thugs driving the van with Nick and Billy in back, one notices that Nick's cane is actually a sword. He then runs his thumb along the non-blade edge of the sword, yet gets cut as if it was the blade edge.
When Nick slices the apple tossed by the Assasin, it is shown to fall with one half leaning on the other. However, in the very next shot, the pieces are at least 2 feet apart.
During the van chase where Nick is driving the van, at one point you can see through the rear view mirror (before it gets shot off) that they just passed the "Reno: The Biggest Little City In The World" sign, but just a moment later (when Nick runs through the red light) you see the big sign coming up ahead.
During the fight at Lynn Devereaux's house, the houseplant atop the china cabinet changes from one kind to another several times between shots.
During the van chase when Nick is driving, Billy accidentally tells Nick to turn right onto supposedly a one-way street, however as they drive down the street, you can see traffic lights on both directions. One-way streets would never have traffic lights facing both directions, and this particular street was obviously a two-way street re-painted to look like a one-way.
Billy has brown eyes while both of his parents have blue eyes. It is impossible for two blue-eyed parents to have a child with brown eyes.
During a fight scene at MacCready's house, Nick loses his sword, which ends up at the bottom of a pool. In the next shot, Sho Kosugi's sword is visible on the deck; some confused it with Nick's.
Nick's digital watch probably did have a feature to speak the time, he just never uses it on screen. Nick is, after all, a very pragmatic character. The non-use of any time-speaking function is likely because the props department could not obtain such a watch.
When Nick cuts off the policeman's hand near the beginning of the film, we see the hand fall to the floor, then the cop falls back, and for a moment you can see he still has his hand.
When the policeman gets his hand sliced off and it falls to the floor, you can see a white wire going from the back of the hand into the floor. This wire is what creates the shot from the gun that the hand is holding.
When Frank answers the phone at Colleen's home and talks to MacCready, you can see that the phone cord is not connected to the phone.
The "girlfriend"'s glasses are made of plain glass.
Obvious manipulation of the film speed during many of the fight sequences.
In the scene where they are being chased under the Reno arch two cars collide in the intersection. This was unplanned yet kept in the film.
Shortly before boarding the bus in Miami, Billy tells Nick, "I get the window seat. You don't need it. You're blind." Nick responds to Billy, saying, "You have me there, little prick," but as he is saying that, his lips do not move.
Immediately after Nick's scenes in Vietnam, he is seen walking down a stretch of highway signed as Florida State Road 84, which is shown as a 2-laned stretch of road. At the time of this movie's production (1988-89), the real SR-84 had already been upgraded to a 4-laned divided highway (just prior to becoming part of present-day Interstate 75).
The photo of Nick and Frank together was taken right before the mortar attack started, after which the two didn't see each other again. How did they both end up with a copy of it?
Nick successfully reaches out to put his hand on a tree when he has just become blind. People who have recently lost their ability to navigate well or stand upright due to physical impairments including intoxication are liable to reach out at random when they suspect they are about to fall over. It is a reflex action and last resort in the hope of avoiding falling on the ground. In this case, it worked.