Arnold's Hat/Stoop Kid - S1-E3
Audio problem: When Harold says, "Hey, what are you, scared?" his mouth stays open for the last word. It never closes for the "d" at the end.
Tutoring Torvald / Gerald Comes Over - S1-E13
Continuity mistake: Arnold and Gerald have to climb stairs to get to Oskar's apartment, but this would mean the building has three floors, and the outside views indicate that there are only two (plus the attic).
Continuity mistake: The first time you see the line of girls, Rhonda's shoes are "low-cut", but just before Helga says "Move it, football head", the shoes suddenly extend much higher (like they normally do in the stories).
Love and Cheese / Weighing Harold - S4-E7
Continuity mistake: Lila was pretty much entirely underwater in a "standing" position when Arnold rescued her, how come suddenly the water only reached her knees?
Tutoring Torvald / Gerald Comes Over - S1-E13
Audio problem: In the scene during recess when Arnold and Gerald are talking about tutoring Torvald, Arnold says, "Ah c'mon, Gerald"; however, when he says, "it's not going to be so bad," his mouth doesn't move.
Freeze Frame / Phoebe Cheats - S2-E8
Continuity mistake: Phoebe Cheats: After Phoebe reads the poem from her book, she sets the book back against the lamp, and it is closed. Then when Phoebe gets up out of her chair, the book is suddenly open. (00:14:05)
Girl Trouble / School Dance - S3-E18
Other mistake: Girl Trouble: When Phoebe says she has costume designs for the Mandans, the Chinook, and Sacagawea, Gerald says, "I could have sworn it was Sacagawea." Then, there is a shot of Helga and Phoebe, but there is a problem with this shot. What we're supposed to see is Helga and Phoebe sitting in their seats at their side of the table. Instead, the background is of Arnold and Gerald's side of the table, while Helga and Phoebe are shown in front of the table, which doesn't make sense. (00:02:31)
Other mistake: Ms. Perfect: After Lila answers Mr. Simmons' question about the inventor of the telegraph, as Phoebe says, "But I knew that," the book on Nadine's desk is overlapping the back of Phoebe's chair. (00:14:07)
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)
Hall Monitor / Harold's Bar Mitzvah - S2-E15
Other mistake: Hall Monitor: When Helga chooses Phoebe to be the new hall monitor, as Phoebe starts walking to the stage, she is briefly layered behind the boy sitting behind her, and she is layered over Joey and the boy sitting next to him. (00:02:31)
Runaway Float / Partners - S2-E20
Other mistake: Runaway Float: After Nick talks about redesigning the parade float, Bob asks the kids who wants to ride on the float. Arnold then tells them it's great the way it is, and when the kids start saying, "Me! Me!", there is an animation glitch where part of Robert's head and hands get stuck in the air for about a second. (00:06:01)
Back to School / Egg Story - S4-E8
Other mistake: Back to School: After Principal Wartz tells Phil he will find a classroom for him, it cuts to a shot inside Mr. Simmons' classroom. If you look at Sid in this shot, the lower half of his body is cut off. Phoebe's right foot is also layered over him. (00:03:58)
Hall Monitor / Harold's Bar Mitzvah - S2-E15
Other mistake: Hall Monitor: During detention, the class helps Phoebe realise how much she has changed. When Helga wipes the window so Phoebe can see her reflection, in the first shot, Phoebe's reflection is not backwards as it should be. (00:10:45)
Hall Monitor / Harold's Bar Mitzvah - S2-E15
Continuity mistake: Hall Monitor: In the first and last overhead shots of the detention classroom, the "fire" sign, the fire extinguisher, and light switch are not on the wall beside the door, though all are on the wall in other shots during this scene. (00:09:30)
Hall Monitor / Harold's Bar Mitzvah - S2-E15
Continuity mistake: Hall Monitor: When Principal Wartz tells Helga she cannot volunteer again, he removes the "revered badge" and its black crossbody strap from Helga. Helga then selects Phoebe as the next hall monitor. When Phoebe joins them on the stage, Helga is again wearing the crossbody strap with the badge in the wide shot, but it's gone in the next shot as Wartz places it on Phoebe. (00:02:10)
Hall Monitor / Harold's Bar Mitzvah - S2-E15
Continuity mistake: Hall Monitor: During the school assembly, Principal Wartz's necktie has diagonal stripes, and its top knot stripes switch to the opposite direction, then revert to the proper direction.
Helga's Locket / Sid and Germs - S5-E7
Other mistake: Helga's Locket: When Helga climbs to the top of the boarding house and looks at Arnold and Grandpa through the window, as Arnold tells Grandpa, "It's embarrassing and weird," Helga's left sleeve is incorrectly coloured pink instead of white. (00:09:02)
Sid's Revenge / Roller Coaster - S3-E8
Other mistake: Sid's Revenge: When Sid is telling the police officer that he killed his school principal, Arnold's pants are the same colour as his skin, and his hat is not coloured in. (00:09:13)
Save The Tree / New Teacher - S2-E1
Continuity mistake: New Teacher: Arnold's classroom door vanishes from its door frame in various shots, then the door reappears in its proper place. That door's doorknob also switches between the right side of the door and the left side a few times.
Curly Snaps / Pre-Teen Scream - S3-E6
Other mistake: Pre-Teen Scream: When the kids are sitting on Arnold's stoop in the beginning, there are two shots where Arnold's pants are the same colour as his skin, giving the sense that he has no pants on. (00:12:03)
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.