Continuity mistake: Venkman meets Dana by a fountain. When he says goodbye to her, first a man with a hat passes behind him and disappears in the next angle; then, in a close-up, Venkman is surrounded by dozens of people who vanish half a second later in the wide angle, where the place appears empty. (00:44:45)
Factual error: Walter Peck in his slimy handshake introduces himself; "I represent the Environmental Protection Agency, the third district." The EPA has no 'districts' (NY's in Region 2). (00:46:15)
Continuity mistake: There's a crumpled piece of paper on the shelves behind Peter when he argues with Walter Peck in his office. As you can observe when Peck sits down, the paper is in a different position in the close-up compared to the wider angle. (00:47:40)
Continuity mistake: The famous Twinkie scene; notice that when Egon utters the line "Let's say this Twinkie represents the normal amount of psychokinetic energy" etc, there's a cut mid-sentence. Harold Ramis is holding the bar with 3 fingers in the first shots, 4 in the second. (00:48:05)
Continuity mistake: When the demon breaks out of the statue on Dana's apartment building, it breaks away the right paw. When we see the statue after the demon is out, both paws are intact. (00:48:55 - 00:51:55)
Continuity mistake: Dana gets home and puts down on the table the paper bag with food and her coat as she answers the phone. She takes her shoes and pants off and the camera cuts away to a different angle where the coat and the paper bag have changed position. (00:51:00)
Continuity mistake: When Dana struggles with the literal arm-chair, one of the arms pops out of the top of the right armrest and a clawed hand clutches Sigourney Weaver's face. Change of camera angle, and not only she is struggling against the demonic limb in a different position, but the hole is gone from the top of the armrest, the arm is sticking from the side. (00:51:45)
Continuity mistake: During the party, when Louis throws the coats on the gargoyle's head, its horns are visible from the front shot, but covered in the immediate angle from behind. (00:53:20)
Continuity mistake: After Louis asks if anybody wants to play Parcheesi at his party, there is a lady sporting a red vest behind him, standing in front of a wall with framed photos. Two shots later, she's standing in front of the kitchen next to a bespectacled man. The very next shot, she's teleported back to where she was initially, in front of the wall. (00:53:25)
Revealing mistake: Tully just ran away from the apartment building screaming. The doorman repeats to an incoming couple "A bear, in his apartment..." The husband pulls his wife back without for a single moment glancing at the direction the beast (or its growl) come from; he stares constantly at the foreground. (00:54:00)
Continuity mistake: When Vinz Clortho sprints off the building's front doors to chase Tully, the distance between the passers-by changes. (00:54:05)
Audio problem: Running away from the 'bear', Tully shouts the humorous line; "I'm gonna to bring this up at the next tenants' meeting...there's not supposed to be any pets in the building." However, look at Rick Moranis' face; his lips are not moving and the line was dubbed over. (00:54:10)
Continuity mistake: Trying to escape the demon dog, Tully trips over a chair and bangs against the windows of the restaurant. You can see in the first shot that the maitre d' (the guy with grey hair and stache, wearing black) is looking at him. But in the reverse shot, he's smiling at the patrons at the table, and only a moment later raises his head to check out what the fuss is about. (00:54:35)
Revealing mistake: After Louis runs out of the building crying "There's a bear in my apartment!", the monster exits the place and knocks down the doorman, but doesn't cast a shadow until it steps on the pavement. (00:54:55)
Continuity mistake: When the possessed Dana asks Peter for the second time "Are you the Keymaster?", Peter comes in; notice that Sigourney Weavers' left hand is still at the top of the doorframe, in the reverse shot it's suddenly down. (00:56:10)
Continuity mistake: During the scene with the possessed Dana in bed with Peter, the pillows rest at different heights against the bed's headboard. (00:57:30 - 00:58:40)
Continuity mistake: When Venkman is in Dana's bedroom the quantity and quality of light coming through the window changes between shots; look at the side of the window when he is counting down, for instance. (00:58:30)
Continuity mistake: When the terror dog ruins Louis' house party, a man cowers behind a dining chair. In the shot immediately following his closeup, the chair has magically sprouted armrests. (00:59:35)
Continuity mistake: Dealing with Tully, Annie Potts says one rather oddly foreshadowing line to Harold Ramis about his death, and then clings to him. Ramis puts a hand on her shoulder, and the position is different in the next shot. (01:02:00)
Character mistake: Peter tells Egon over the phone that he gave Dana "300 cc of Thorazine." Besides the funny implications the movie ignores on how and why he was in possession of it, Venkman says "cc", but the drug is dosed in mg, so at the very least Venkman misspoke (that'd be 1/3 liters!). The line is not in the shooting script and other sources like the novelization just say that Dana had some valium lying around. (01:02:30)
Answer: Ron Jeremy can be seen in the crowd outside the firehouse right after the containment unit is shut off.