Plot hole: Diabolik blinks in Morse code to his accomplice the location of one of his hidden stashes. He says it's in 'the third brick to the left' and the street name, but no address or other reference. She (who previously knew nothing about the location) finds it immediately. It's worth noting that the movie is a faithful adaptation of a couple issues of the comic, but this bit of subplot is a fresh addition and the original hiding spot in the 1963 issue was a plausible one (cave behind a specific waterfall).
Factual error: When pit bull Shadow was chasing Phoenix, the distances between them varied - even appearing to increase - but the pit bull should have been able to quickly close the gap and catch Phoenix. In general, an adult person (about 7 mph) cannot outrun a pit bull (25-30 mph). Also, unless Shadow was trained to stop pursuing Phoenix if she got over the fence, pit bulls are actually quite good at climbing fences. (00:02:38)
Revealing mistake: The "bridge" within the crime scene tape is obviously a prop. It should be a continuation of the road, but it is tilted to the left and is more vertical (around 45°). The bridge isn't even very high. When Byron and others go under the bridge to look at the dead girl, there is only a few feet above their heads (clearance under the bridge). (00:04:54)
Other mistake: The chances that no-one in the approaching truck - three men, including a man standing in the bed facing oncoming traffic - would notice that Danny had a front seat passenger are very low, if not zero. Even after Motley got into the second row seat of the truck, but did not get down right away, the men in the truck had turned around and were following Danny but still did not notice Motley. (00:10:00 - 00:10:27)
Continuity mistake: Joe has 'Rick C' (his partner) listed as a contact in his phone - late on in the movie when Joe calls him from the bathroom stall, he is listed as just "Rick"
Continuity mistake: The door had multiple small rectangular glass panes enclosed in wood frames, but the glass pane that Alan Schaefer's head/body went through was larger and no wood frames were visible. (00:40:28)
Other mistake: William Tillich (AKA Bill Tell) had one suitcase which could not possibly hold enough sheets (or thin blankets) to cover/wrap all the furniture in his motel room like he did. (His suitcase was not very large and also contained his clothes.) He covered an even larger area of furniture in Gordo's house. It isn't clear if he used his own sheets or just happened to find the same kind in Gordo's house.
Deliberate mistake: The view looking out the windshield showed the man on the bicycle had stopped when he was in front of the car's passenger side, but the outside view showed the man still coming to a stop and then tilting his bicycle. (00:07:12)
Factual error: After Ressler tells McChesney he wouldn't be surprised if one day she's tracking down sequence killers, McChesney replies, "Not sequence killers. Serial killers. That's what they should be called." But it was Ressler who claimed he coined and is often credited with coining the term "serial killers" (at least in the U.S). ** After showing pictures of some of Bundy's victims, Ressler is shown and it is pointed out, "He [Ressler] is credited with coining the term 'serial killer'." (1:31:30). (00:26:40)
Other mistake: Blood gushed out of the bound man's lower inner arms that were slit with a knife from below the elbow to the wrist (then turned toward the ground). A switch to an aerial view showed no additional blood dripping (while he was still alive). Also, blood would not pour out of his arms to the ground in a horizontal stream like it did. (00:02:04 - 00:02:27)