Revealing mistake: When Arnie uses the dead body as a human shield, watch the corpse's mouth - he grimaces every time he gets hit (the squibs hurt). (00:31:00)
Plot hole: When Arnie is taking off his woman's head he presses a switch by the ear and the ear comes out. The device reaches right inside the fake head and there would be no room for Arnie's real head. (00:46:00)
Continuity mistake: When Arnold Schwarzenegger and Rachel Ticotin are being attacked by the giant drilling machine, Arnie grabs a pneumatic drill and cuts the main oil line of the machine, getting the left side of his face and his shirt doused in oil. Yet throughout the remainder of the film, there is no oil on Arnie's face or shirt. (01:39:55)
Continuity mistake: When Arnie uses the hologram projector in the alien reactor, there is a brief shot of him facing his own hologram image. Note that the gun and the projector switch positions in Arnie's hands - the bloodstain on his shirt's sleeve does not. (01:37:55)
Continuity mistake: In the escalator scene when Arnie uses a corpse as a shield, there's a close-up of Arnie's gun firing, and we can see there's blood on the side of the corpse's head. However, in the wider shots there isn't. (00:31:00)
Continuity mistake: When Arnie meets Bennie, he takes him to his cab and opens the door for him to get in. At that time, there's an explosion, and Bennie pulls the door down to shield himself and Arnie. The camera switches to behind them, and Bennie is just now pulling the door down. (00:52:50)
Revealing mistake: When Arnold jumps through the glass, you can definitely see a change in his face and body shape. (From the stuntman). (00:30:05)
Other mistake: The title 'Publicity' is misspelled as 'Publicty' in the end credits. (01:46:30)
Continuity mistake: When Arnie comes home after killing his workmate, he pulls Sharon Stone to the floor. From one angle his hands are on her shoulders, from another they're on her elbows. (00:23:45)
Revealing mistake: When Lori punches Doug in the crotch, you can see that Arnold Schwarzenegger is wearing some kind of padding under his pants to soften the blow. (00:25:35)
Continuity mistake: When Doug is running from the bad guys after finding out what was going on from his "wife", he tucks his big gun in to his jacket pocket. When he is running through the scanner, that big gun is now in his pants. (00:28:15)
Revealing mistake: In the scene in the Mars Air/Spaceport, the troops are wearing Casio scientific calculators on their wrists. (00:43:50 - 00:46:55)
Revealing mistake: When Quade shoots Dr. Edgemar, Lori yells "Now you've DONE IT.", and the wall explodes, which is plainly made of foam. Many of the pieces of 'wall' tumble lightly across the floor. (01:05:40)
Continuity mistake: In the scene where Quaid unfolds a flyer for The Last Resort, he unfolds it with the flyer image facing the camera. When the scene cuts to him looking at it, the flyer image is facing him. (00:52:00)
Continuity mistake: When Quaid enters George/Kuato's private room in the rebel base you can see George's desk has a different arrangement from one shot to the other with Quaid's gun disappearing, a blue container swapped with a white on, the computer's screen having a cable plugged in or out and other objects moved around. (01:16:00)
Continuity mistake: When Quaid takes off his old woman disguise and throws the head to a soldier who catches it, the close-up shows that he's holding it beneath the ears. In the wide shot, he's holding it from behind the skull.
Answer: It depends on whether you choose to believe the events of the film are real or in Quaid's lobotomized brain. If the events are real (i.e. Quaid is actually Houser with his memories blocked) then Harry is from the agency and is there to make sure Quaid doesn't say or do anything that would potentially break his memory block (like going to Recall). If you believe everything is in Quaid's mind after he goes to Recall, then Harry really was just his friend.