Continuity mistake: When Arthur sits down to talk about the deodorant with Doug, Doug's hand is flat on the table. Camera changes and it's now on the doughnut box. (00:11:00)
Continuity mistake: When Doug Tells Carrie to pack for Atlantic City the cushion is either on or off her lap. (00:17:15)
Revealing mistake: When Carrie holds the paper towels, the kitchen's curtains over the sink are normal, the window is closed and the blinds are down. However, next shot the blinds are up, the double-hung window is oddly open outward sideways, and the curtain is pulled back with a large clamp. Then it's all back to the normal previous way.
Visible crew/equipment: At the start when Carrie says says "it's already 20 of" look at the screen right to see the kitchen cabinets swing into place as the crew replace them. (00:00:35)
Audio problem: When Doug goes to the door to call for Uncle Hank, the audio is over dubbed. (00:04:05)
Visible crew/equipment: When Spence is leaving after dropping off the pictures a stage light is reflected in the door. (00:08:50)
Visible crew/equipment: After Spence gets weird while taking pictures of Sara at the anniversary party, when it cuts to the wide shot as Arthur says, "Okay, Garver!" a camera is visible at the right side of the screen.
Head First - S1-E6
Audio problem: Doug calls Arthur near the start and the audio is overdubbed. (00:03:15)
Head First - S1-E6
Continuity mistake: When the gang walk into Coopers, a woman and man are talking outside on the street. When the camera changes to focus on Arthur a second man has appeared next to the other two and should have been visible in the first shot. (00:03:40)
Head First - S1-E6
Revealing mistake: When Doug is making breakfast it's clear there is no flame coming from the gas hob. (00:08:15)
Head First - S1-E6
Continuity mistake: When Doug and Deacon are having breakfast in the kitchen, the door keeps changing from open to closed with no-one touching it. (00:08:30)
Head First - S1-E6
Continuity mistake: During the poker game, Arthur teases Spence because he's a virgin, which is mentioned later when Doug tells Cariie, "He teased him about the virgin thing." But in one of the later episodes, it is mentioned that Spence had an affair and had sex with his Home Economics teacher when he was very young and had long hair.
Visible crew/equipment: At the start, while Doug and Carrie are in the jewelry store, in the shot of Doug swinging the shopping bags at the overhead surveillance camera, we can see a production camera at the left side of the screen. Then in the next shot, from the POV of the surveillance camera, the edge of the store's set is visible at the right side of the screen. (00:02:05)
Visible crew/equipment: During the driving scene at 00:07:35 you can see a stage wall on the set to the right when the lights pass over the car. (00:07:35)
Revealing mistake: When they first drive to their class, we see the street lights behind them. When Carrie pulls over to pick up Spence, she turns the steering wheel, but the lights in the back don't turn. (00:07:45)
Continuity mistake: During both driving scenes, the street lights in the background do not fade away in the distance to indicate they are actually driving forward. When Doug, Carrie and Arthur are pulled over waiting for Spence (and again when waiting for Arthur at Dairy Queen), lights scroll over the car and the sound of a passing vehicle can be heard but no car is seen to pass by or drive away in the distance. (00:07:45)
Continuity mistake: In the first classroom scene there are two people sat to Doug's right. These people then vanish a few seconds later. (00:07:55)
Suggested correction: Spence did have sex with the teacher, but the episode with the teasing at the poker game, Arthur and the guys don't know about her yet. Therefore, to their knowledge, Spence is a virgin, and for some reason, he decides not to defend himself with the teacher story.
The episode with them playing cards wasn't the only season 1 episode where Spence's virginity had come up. In season 1, episode 12, Carrie fixes Spence up with a coworker. When Richie and Doug tease him that they've already been together a month without sex they say: "Do you believe this guy?" "A month, huh?" Spence replies: "Yes a month! A month is not that long not to have had sex." To which Doug says: "Yeah, but if you add in the other 31 years, I'd think you'd be a little antsy." Also a little later in the conversation, when Doug tries to convince Spence that he and the girl have sex in his garage: "I'm just saying, if you wait too long, this opportunity could go bye-bye. Then it could be, hey, another 31 years before this opportunity comes again. It's pretty tough losing your virginity when you're 62." So Spence later already having lost his virginity in high school is a continuity error that they just overlooked and alas instances like these become apparent pretty often when you rewatch the show (like Carrie becoming an only Child, Arthur being said to be a great piano player in a season 1 episode while he can't play a single tune in a later season etc., etc).