Character mistake: The first time Arnold tries Rhonda's marriage predictor test, he says his favorite number is five, but Rhonda actually makes six moves. The second time, Arnold says it's three, but Rhonda counts off four.
On The Lam / Family Man - S5-E17
Character mistake: In the wrestling match, the bell rings after the referee counts to 3 - but he's counting while a wrestler is on the mat stomach-first; a pin requires the loser to be on his back.
On The Lam / Family Man - S5-E17
Other mistake: A security guard in the train yard is drinking from a carton of milk depicting the boys. However, they had only been declared missing that afternoon. It is impossible to put out milk cartons that quickly.
Grandpa's Packard / Phoebe's Little Problem - S5-E19
Continuity mistake: Phoebe's Little Problem: When Phoebe tells the lunch lady what she wants and she questions her choices, the lunch lady is standing behind the counter, as she should be. When she is shown again two shots later, she is standing in front of the counter, when she should be behind it. (00:04:03)

Grandpa's Packard / Phoebe's Little Problem - S5-E19
Other mistake: Phoebe's Little Problem: When Arnold goes into Phoebe's room to cheer her up, the birdcage is reflected in the mirror on the wall, but the birdcage is too far to the right of the mirror, so it shouldn't be reflected. This error is shown again in a later shot where Phoebe tells Arnold, "And I'm very good at checkers." (00:09:13 - 00:09:45)
Grandpa's Packard / Phoebe's Little Problem - S5-E19
Audio problem: Phoebe's Little Problem: When Harold wets his pants at the end, Stinky can be heard saying, "Harold wet his pants," but in the shot, he is actually laughing. (00:11:39)

Simmons' Documentary / Big Bob's Crisis - S5-E20
Continuity mistake: Simmons' Documentary: When Mr. Simmons explains the documentary and the kids leave the classroom, Arnold is holding a purple book. In the next shot, it changes direction while in his hand. (00:01:50)

Simmons' Documentary / Big Bob's Crisis - S5-E20
Revealing mistake: Simmons' Documentary: When Phoebe asks Mr. Simmons, "If we're required to do book reports, do we need to choose a book?", her mouth disappears twice. This is easier to see in slow motion, but it's still visible at normal speed. (00:04:27)

Simmons' Documentary / Big Bob's Crisis - S5-E20
Continuity mistake: Simmons' Documentary: Rhonda wears a black top and red skirt on the day of the documentary, but in one shot, she is wearing her regular outfit. She is also wearing her regular outfit in one shot when the class is watching the documentary. (00:06:12 - 00:11:16)
Simmons' Documentary / Big Bob's Crisis - S5-E20
Other mistake: Big Bob's Crisis: When Bob faints at the restaurant and first appears as an angel, his eyes become the same colour as his skin twice. (00:13:58)

Simmons' Documentary / Big Bob's Crisis - S5-E20
Character mistake: In the credits, Anndi McAfee's name is misspelled as "Anndi McAffee." (00:22:58)
Timberly Loves Arnold / Eugene, Eugene! - S5-E22
Continuity mistake: Timberly Loves Arnold: Throughout the beginning scene where Timberly is asking Gerald if she can come along with him, the blue accessories in Timberly's hair keep disappearing and reappearing. (00:01:07 - 00:01:42)
Timberly Loves Arnold / Eugene, Eugene! - S5-E22
Continuity mistake: Timberly Loves Arnold: When Timberly asks Arnold if she can hold his hand while crossing the street, Iggy is looking at Arnold. In the next shot, he is suddenly looking away from him, then goes back to looking at him. (00:02:53)

Timberly Loves Arnold / Eugene, Eugene! - S5-E22
Continuity mistake: Timberly Loves Arnold: When Timberly and Arnold start crossing the street together, Iggy is standing far away from Rhonda and Sid. In the next shot, he is closer to them. (00:02:57)

Timberly Loves Arnold / Eugene, Eugene! - S5-E22
Continuity mistake: Timberly Loves Arnold: When Gerald says, "I could go for some Arnold lemonade," and Arnold pulls him in the alleyway, there is a building with a sign with the word "shoe" on it, written in red. In the next shot, it changes to yellow. (00:04:07)
Timberly Loves Arnold / Eugene, Eugene! - S5-E22
Revealing mistake: Timberly Loves Arnold: When Lila tells Arnold that it's sweet that he is hanging out with Gerald's sister, the stripe on her shirt is layered over her gold button for one frame. (00:05:33)

Timberly Loves Arnold / Eugene, Eugene! - S5-E22
Continuity mistake: Timberly Loves Arnold: Throughout the scene where Arnold, Lila and Timberly are at the lemonade stand, Lila is wearing her gold button on her shirt. When Timberly asks Lila if she wants to come to the baseball game, as Lila says, "I'm sure that I'd love to," she moves her hands, and for a brief moment, you can see that she is not wearing her gold button. (00:05:46)
Timberly Loves Arnold / Eugene, Eugene! - S5-E22
Revealing mistake: Timberly Loves Arnold: When Lila says, "That is, if Arnold doesn't mind making it a threesome," her left eyelashes disappear for one frame. (00:05:50)
Timberly Loves Arnold / Eugene, Eugene! - S5-E22
Other mistake: Timberly Loves Arnold: When Harold is leaving the field after the baseball game, he vanishes while on screen without fully leaving the frame. (00:06:15)

Timberly Loves Arnold / Eugene, Eugene! - S5-E22
Continuity mistake: Timberly Loves Arnold: When Arnold, Lila, and Timberly are in the field together after the baseball game, Lila helps Arnold up and looks at her watch, which she wasn't wearing previously. Then, when Lila starts walking Timberly home, her watch has vanished from her wrist. (00:06:35)
Answer: The show is based in present day times. Plus most cars aren't old fashtioned, I recall seeing a limo and not to mention a cherry picker, etc.