The Aptitude Test / Oskar Gets a Job - S3-E9
Continuity mistake: In "Oscar Gets a Job", Oscar goes around asking people for money. When he talks to Ernie, you can see that there is a phone and a light to the right of the door. When Arnold confronts Oscar in the hall, you can see Ernie's room (7). The phone has disappeared.
Magic Show / 24 Hours to Live - S1-E18
Continuity mistake: The boarding house has a downstairs bathroom, but in "Gerald Comes Over", there's only one bathroom and it's upstairs.
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)
Continuity mistake: Ms. Perfect: When Lila and her father are eating dinner, Lila's spoon is in her can of beans in one shot. When the angle changes and her father says, "You sure are quiet tonight," her spoon disappears from the can of beans (the flap of her can of beans is also layered under her father's left arm), then reappears in the next shot. (00:19:05)
Continuity mistake: Helga makes Arnold sit in a plate of chocolate pudding as a prank, leaving a huge chocolate pudding stain on the back of his shirt. Then, when Arnold picks up the gift box from Grandpa and returns to the cafeteria, the chocolate pudding is gone from his shirt but reappears later on when Arnold and Helga are at Slausen's Ice Cream. (00:12:37)
Operation Ruthless/The Vacant Lot - S1-E7
Continuity mistake: Operation Ruthless: When the Cheese Festival is first shown, Arnold and Gerald are standing at the bumper car ride, but in the next shot, they are suddenly standing in a different location, which seems to be at the green building from the beginning of the episode. (00:03:12)
Love and Cheese / Weighing Harold - S4-E7
Continuity mistake: Love and Cheese: When the sign for the Built-To-Hurl is first shown, it is spelled with a hyphen between "To" and "Hurl." When the sign is shown again, that hyphen is missing, then reappears a moment later. (00:07:19)
Abner Come Home / The Sewer King - S1-E16
Continuity mistake: Abner Comes Home: Some of the objects and other things in the Sunset Arms backyard disappear, reappear, change, or move around in various shots. (00:11:27)
Curly Snaps / Pre-Teen Scream - S3-E6
Continuity mistake: Pre-Teen Scream: When Phoebe shows up at Helga's house to pick her up for the concert, Phoebe is wearing a red outfit with a red scrunchie in her hair. Thereafter, for the rest of the episode, her red scrunchie changes to her normal yellow one in some shots. (00:15:46)
Downtown as Fruits / Eugene's Bike - S1-E1
Continuity mistake: Downtown as Fruits: After Arnold and Gerald arrive at the school, it cuts to Helga crying about her play being ruined. When Phoebe taps her, her left arm is coming from the side of her cheese costume, but when the angle changes, it's coming from the front of her costume. (00:10:43)
Continuity mistake: Ms. Perfect: When Lila goes to Patty's locker, the books she is holding constantly change. First, she is holding two books, then three, then the red book is suddenly on top, then the red book disappears and the rectangle on the brown book changes to white, then it goes back to yellow and the blue book gets replaced by the red one, and finally, the blue book reappears (she is also suddenly not holding the locker handle, and the way she holds the books changes). (00:15:48)
Continuity mistake: Ms. Perfect: When Patty opens her locker and the jello falls on her, her head is raised above the floor, and there is no jello on her head. In the next shot, her head is on the floor, and there is jello on her head. (00:16:24)
Love and Cheese / Weighing Harold - S4-E7
Continuity mistake: Love and Cheese: At the end, Arnold says to Lila that he will walk her home. In the next shot, a janitor suddenly appears behind them. (00:11:40)
Monkeyman! / Buses, Bikes and Subways - S5-E1
Continuity mistake: Buses, Bikes, and Subways: Helga wears a watch on her right arm throughout the episode. However, when Helga approaches Sheena's uncle Earl and wakes him up, her watch is missing, then reappears when Earl's boat sinks. It disappears again when Helga comes up from the water, then reappears a moment later. (00:18:59)
Helga's Masquerade / Mr. Green Runs - S5-E2
Continuity mistake: Helga's Masquerade: When Helga and Lila are at Slausen's Ice Cream, after Helga asks Lila how she can learn to act so nice to people, she grabs her milkshake with her left hand. A shot later, she is now holding it with her right hand, and a spoon appears in her left hand. (00:03:30)
Helga's Masquerade / Mr. Green Runs - S5-E2
Continuity mistake: Helga's Masquerade: When Helga and Lila are at Slausen's Ice Cream, after Helga asks Lila where she gets her material from, Lila's right arm is below the table, but a shot later, it's above the table, and a spoon appears in her hand. (00:03:18)
Arnold's Thanksgiving - S3-E14
Continuity mistake: When Helga is backstage preparing for the play, there is an "H" on the left side of her costume. When Phoebe tells her that she's on, she turns around and the "H" is not on her costume, then reappears a moment later. (00:03:32)
Arnold Visits Arnie / Chocolate Boy - S5-E12
Continuity mistake: Arnold Visits Arnie: In the country store, when Arnold says, "But, what about Arnie?" and it cuts to Arnie counting the bubble gum, the "1893" on the window is red but changes to white in the next shot. The "Est." also disappears. (00:05:53)
Arnold's Thanksgiving - S3-E14
Continuity mistake: When Arnold's family is sitting around the table on Thanksgiving, there is a blue bowl with a spoon in it where Arnold is sitting. A few shots later, the bowl changes to white, and the spoon is gone. In the next shot, the bowl is blue again, and the spoon is back. In the shot after that, the spoon disappears again. (00:06:34 - 00:07:08)
Arnold's Thanksgiving - S3-E14
Continuity mistake: When the play finishes and all the kids are standing on stage, Arnold and Helga are holding hands. Arnold looks at Helga, and Helga pulls her hand away. When the shot changes, they are holding hands again. (00:05:17)
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.