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)
School Play - S3-E19
Continuity mistake: Lila's collar is gold throughout the episode. When the girls audition for the part of Juliet and Mr. Simmons says that they were all very good, her collar is white, and her gold button is missing. Then when Mr. Simmons says Lila will be the third understudy, her collar is gold again, but her button remains missing. Later on, when Mr. Simmons announces Lila will take the role of Juliet, her collar is white again, and her gold button is missing again. (00:08:46 - 00:14:26)
School Play - S3-E19
Continuity mistake: When Helga tries to convince Lila to drop out of the play, as she says, "What about that crazy costume you have to wear?", Lila's gold button is missing. It's also missing when Lila says, "I'm sorry, Helga, you're mumbling." (00:15:42 - 00:17:06)
Continuity mistake: Mugged: Throughout the scene with Arnold and Grandma on the bus, Arnold is not wearing his hat. When the creep runs off the bus and the camera shows Arnold and Grandma from outside the bus, Arnold is wearing his hat. (00:11:35)
Beaned / Old Iron Man - S5-E11
Continuity mistake: Beaned: When Arnold is walking Helga to school and she sees some flowers, they are both standing on the sidewalk. Two shots later, they are on the road. Also, when Arnold walks up to Helga, he is in mid-air, and when Helga stands up, she is also in mid-air. (00:05:53)
Hall Monitor / Harold's Bar Mitzvah - S2-E15
Continuity mistake: Harold's Bar Mitzvah: In the beginning, when Stinky asks Harold if he wants to play stickball, there is no wristband on his arm. Harold says he has to go do his lessons, and in the next shot, a wristband appears on Stinky's arm, then disappears. Later on, when Harold comes out of the synagogue, his wristbands are back on his arms. (00:12:03)
Full Moon / Student Teacher - S4-E1
Continuity mistake: Full Moon: Throughout the episode, Harold's eyes change from yellow to white during a few consecutive shots, as well as mid-shot.
Full Moon / Student Teacher - S4-E1
Continuity mistake: Full Moon: When Arnold leaves the school at the beginning, he is carrying a green book. A few seconds later, the rectangle on the cover changes to white, then back to green. (00:03:14)
Full Moon / Student Teacher - S4-E1
Continuity mistake: Full Moon: When Principal Wartz tells Arnold to see him every day after school for the next four weeks, the words on his office door are yellow. About a second later, they change to red, then back to yellow. (00:02:57)
Tour de Pond / Teachers Strike - S2-E18
Continuity mistake: Tour de Pond: When Rex's grandfather walks up to Arnold's Grandpa at the end, his badge has eight squares on it, but in the next shot, it changes to four stripes. (00:11:20)
Tour de Pond / Teachers Strike - S2-E18
Continuity mistake: Tour de Pond: When Rex notices that Arnold's boat is winning and starts running, the red and yellow squares on his grandfather's badge change to red and black. (00:10:18)
Tour de Pond / Teachers Strike - S2-E18
Continuity mistake: Tour de Pond: When Gerald puts the boat made out of the block of wood in the fish tank, the sail is pointing towards the right, but when the boat sinks, it's pointing towards the left. (00:02:18)
Tour de Pond / Teachers Strike - S2-E18
Continuity mistake: Tour de Pond: When Arnold makes a boat out of a block of wood, there is a blue cup on the newspapers with gray scissors and another orange object in it. In the next shot, the cup becomes green, and the scissors and other object become pink. As the scene continues, they change colours a few more times. The pencils also become the same colour as the newspapers. (00:02:11 - 00:03:49)
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.