Other mistake: Spence eats some peanut M&M's despite being allergic to peanuts. (00:01:40)
Suggested correction: This episode was very early in the series, before knowing any history of the characters. Spence's peanut allergy came up in much later episodes. It is possible that he developed the allergy later.
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.
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).
Fixer Upper - S1-E12
Continuity mistake: After Spence suffers from his allergic reaction to peanuts he's seen lying on the couch. Doug then says something to the effect of having to scrape Spence's lunch off the fence, indicating that he threw up. But the allergic reaction took place before they got to the lunch.
Revealing mistake: Carrie comes into the kitchen, visibly hot and sweaty, and says, "Could it be any hotter?" Doug also has a sweat stain on his back and they stick their heads in the freezer. Suddenly Arthur walks in and says, "Do I have the word pushover on my forehead?" Arthur is wearing a thick shirt tucked into long pants and yet is not sweaty. At his age he would be more visibly drained from the heat than both Carrie and Doug. This happens again later in the episode in the garage.