Revealing mistake: Almost every time Sam looks in a mirror or the viewer sees Sam in a mirror, the movements of Sam and Sam's "reflection" hardly ever match up correctly as if it were Sam's real reflection.
Revealing mistake: Al is supposed to be a hologram. However, he is constantly casting shadows, and as a projection, he shouldn't.
Factual error: Many of the episodes are set in the 1950's or early 1960's, but we always see three-prong electrical outlets in the buildings. Three prong electrical outlets only came into common use in the mid to late 1960's, and were required starting in 1969. While they existed before that, they were only installed in specific use situations.
Genesis (1) - September 13, 1956 - S1-E1
Revealing mistake: Tom/Sam's wife and her reflection on the mirror do not match. The reflection moves her head, but the real person does not do that. (00:06:40)
Genesis (1) - September 13, 1956 - S1-E1
Continuity mistake: The shaving cream smeared on Sam's face looks nothing at all like the cream on his reflection's (Tom's) face in the mirror. (00:08:00)
Genesis (1) - September 13, 1956 - S1-E1
Continuity mistake: When Al is standing next to the juke box, Sam walks over to make a selection, and when Al starts talking his reflection is visible on the glass. Later in this episode, Sam is talking to Al at the sink of the dressing room at the ball park. As Sam looks into the mirror he says he thinks Al is a vampire, to which Al replies, "Neurological holograms don't reflect, Sam." (00:26:00 - 01:15:30)
Genesis (1) - September 13, 1956 - S1-E1
Continuity mistake: Al casts a shadow on the airplane. That's should not occur, since Al is a hologram. (00:50:05)
Genesis (1) - September 13, 1956 - S1-E1
Continuity mistake: A confused Sam/Tom stumbles out into the yard bare-chested with shaving cream smeared on his face and neck. In the next shot, though he hasn't touched it, the cream is suddenly all over his chest as well.
Genesis (1) - September 13, 1956 - S1-E1
Continuity mistake: In the shower, the Burma Shave cream on Sam's face changes from being partially washed off to being thick and foamy, then back to partially washed off.
Genesis (1) - September 13, 1956 - S1-E1
Continuity mistake: Al is talking to Sam near the hanger about his options regarding the pilot. When we see Sam and the back of Al's head, there is a significant shadow on Al. It isn't there in the opposite angle. On top of that, since Al is a hologram, shadows shouldn't affect him.
Genesis (2) - September 13, 1956 - S1-E2
Deliberate mistake: When Sam ejects and lands on the ground, the closeup is a flipped shot, note the "US Air Force" is backwards on Sam's helmet. (00:19:10)
Genesis (2) - September 13, 1956 - S1-E2
Continuity mistake: When Sam ejects from the X-2 and parachutes to safety, he lands on the desert floor and the chute comes down on top of him, covering him completely. In the very next shot, we see him lying face up and the parachute has entirely disappeared.
Star-Crossed - June 15, 1972 - S1-E3
Revealing mistake: Sam stares at himself in the mirror and takes out his wallet to determine who he's leaped into. But the "reflection" in the mirror lowers the wallet and looks back up before Sam does. (00:05:20)
The Right Hand of God - October 24, 1974 - S1-E4
Continuity mistake: Near the beginning, Sam has a cut on his left eye from the fight which they apply a bandage to later. The cut briefly disappears when Sam is talking to the sister, only to reappear.
The Right Hand of God - October 24, 1974 - S1-E4
Other mistake: In the locker room, the old man's hair is pulled down over his right eye, away from the mirror as his right side is toward the wall. In the reflection, his hair is facing toward the mirror over his left eye, rather than away over his right.
The Right Hand of God - October 24, 1974 - S1-E4
Revealing mistake: As Sam looks in the mirror, the trainer's reflection puts its right hand on Sam's right shoulder a split second before the camera view hand.
How the Tess Was Won - August 5, 1956 - S1-E5
Continuity mistake: Though he's leaped into someone else, we always see Sam as Sam, dressed in all the host's clothes (including glasses or sunglasses). His host is revealed only in reflections. But here, when he looks at his host-self in the mirror, the hat and clothes are all identical - except that the reflection is wearing glasses, and Sam isn't. (00:43:00)
Double Identity - November 8, 1965 - S1-E6
Factual error: The episode takes place November 9, 1965. After the haircut incident they are seen moving away from a theater with Doctor Zhivago on the marquee, but the movie was released December 22, 1965, a month and a half after the scene is supposed to take place. (00:28:00)
Double Identity - November 8, 1965 - S1-E6
Revealing mistake: Sam's reflection character turns around too slowly in the mirror at the beginning of the episode.
The Color of Truth - August 8, 1955 - S1-E7
Continuity mistake: After Miss Melanie's son leaves, Sam/Jessie reaches out to steady her. His left hand is on her shoulder until the camera angle changes, when both his hands are at his sides. Change angles again, and his hand is back on her shoulder.
Chosen answer: Per the Quantum leap page at http://www.scifi.com/quantum/episodes/season5.html. 8 August 1953: An enigmatic leap lands Sam in a Pennsylvania tavern, as his own grown self on the day of his birth. As Al and Gushie work frantically to locate him, Sam befriends a wise bartender (popular character actor McGill, who'd appeared in a different role in the very first "leap") and a group of coal miners. As a host of familiar-looking faces pass through the bar - with different identities than Sam remembers - Sam ponders his life of leaping with Al the bartender, who tells Sam he controls his own destiny. Pressed for more, Al the bartender simply shrugs and says, "Sometimes, 'that's the way it is' is the best explanation." Sam realizes he must right at least one more wrong before he can go home, and leaps back to tell Al Calvavicci's wife Beth (from "M.I.A.") to wait for Al, who will survive Vietnam and come home to her. The closing title cards state that Beth and Al have four daughters and will shortly celebrate their 39th wedding anniversary ... and that Sam Beckett never returned home.
Boobra