Audio problem: When Shelly is being wheeled away in the beginning, she makes a strained gasping sound right before they put the oxygen mask back on her. But her gasp doesn't match her mouth movements. In fact, it's impossible to make the sound she made with the mouth movements she made. Try it yourself. It almost looks like she's saying "F**k" or something similar, and they just dubbed it over with a gasp. Additionally, the gasp is far too loud and clear given how softly she's speaking. Bad looping.
Deliberate mistake: When Eric first enters his old apartment, watch very closely. When he first wanders in the room, his body has a slightly weird jitter and blur to it that doesn't quite match his movements. This is because the footage of Eric walking through the doorway is actually taken from the scene in the alley. They "cut" Brandon Lee out of that scene and inserted him into the apartment since they didn't have a shot of him. But unfortunately, it has some odd "glitches" due the footage not quite matching.
Visible crew/equipment: When Eric disappears for the first time the camera spins around on Albrecht. In this shot, the shadow of the camera can be seen at his feet. (00:31:50)
Other mistake: When the girl is kidnapped and Eric goes to save her, he enters a big door of that Gothic cathedral (as depicted on the movie cover). At that moment, the wind blows. But for the scene to make any sense, the wind should blow from the outside in, not from the inside of the church out, but the motion of Eric's hair shows the wind blowing the wrong way. (01:05:55)
Answer: Top Dollar (the main villain played by Michael Wincott) sent them over there to talk them. He sorta explained at the end. He 'believed' that he owned the building. I think he said something along the lines of: "Hell, nothing in this area happens without my say so." I guess Eric and Shelly's complaints were going to attract attention with the authorities and Top Dollar did not want that.
XIII