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).
Olga Comes Home / Sally's Comet - S1-E15
Continuity mistake: In Sally's Comet when Gerald, Arnold, and Grandpa are in the traffic jam on the way to Hawk Mountain the position and type of cars around them change. When we first see the car there is a truck there and no room for them to turn around. When they do turn around then there is room and the truck is gone.
Abner Come Home / The Sewer King - S1-E16
Continuity mistake: Abner Come Home: When Abner comes back to the boarding house at the end, Arnold starts running towards him, and there is no mud puddle. In the next few shots, a mud puddle suddenly appears for both of them to fall into and roll in. Then in the next wide shot, the mud puddle disappears, and in the last two shots of the episode, it returns once again. (00:11:09 - 00:11:48)
Abner Come Home / The Sewer King - S1-E16
Continuity mistake: Abner Come 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)
False Alarm / World Records - S1-E17
Continuity mistake: In "World Records", during Arnold's inspirational speech on the stoop of the boarding house, Gerald is sitting on the railing. He changes positions from sitting facing Arnold on the steps to facing the street between shots.
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.
Continuity mistake: Arnold's glass roof is covered in snow after he can't find the boots, and he is depressed. Immediately, he looks up, and there is no snow. We see through the glass to open sky.
Continuity mistake: When Helga is talking about Arnold, the computer store she is in front of is on a corner (Phoebe is seen going around the corner) but a few shots later the store is no longer on a corner.
Save The Tree / New Teacher - S2-E1
Continuity mistake: New Teacher: At the start, Principal Wartz writes Mr. Simmons' name on the chalkboard. Then, when Mr. Simmons walks over to the desk, the writing is missing from the chalkboard; it reappears a moment later. (00:12:07)
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.
Save The Tree / New Teacher - S2-E1
Continuity mistake: In the beginning of 'Save The Tree', the tree ladder is a distance above the ground. Later on in the episode, when Arnold and his friends go to the tree house for the last time, the ladder is practically touching the ground.
Save The Tree / New Teacher - S2-E1
Continuity mistake: When Harold eats Mr. Simmons' tomato sandwich, there is a red stain from the tomato on Harold's desk. This stain disappears in later shots.
Save The Tree / New Teacher - S2-E1
Continuity mistake: In New Teacher when the principal is telling the class about their new teacher the students switch seats between shots.
Longest Monday / Eugene's Pet - S2-E4
Continuity mistake: In "Longest Monday" at one point in the episode, Arnold and Gerald run off of a bus and down an alley. Two fifth graders come chasing after them. In the next scene, you see Arnold and Gerald hiding in the sewer under the 5th graders. Arnold then crawls through a very narrow tube, and Gerald follows. You then see the end of the tube and Gerald come out of the it first, and Arnold climbs out last. It would be impossible for Arnold and Gerald to switch places inside the tube because it was way too narrow.
Continuity mistake: Ms. Perfect: When Lila is wearing her new blue outfit at recess, she wears light blue bows in her braids, but when she is shown in close-up, she is wearing her regular green bows. There is also a small animation glitch with Lila's right bow. (00:15:22)
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)
Continuity mistake: Ms. Perfect: At the start of the scene where Lila gets pranked, the table has its flap down, there are four chairs around it, and there is nothing on it. When Helga walks Lila over to the table, the flap is up, there are only two chairs around it, and a "Reserved" card appears on it. When Lila runs out of the cafeteria, there are four chairs around the table again. (00:18:06 - 00:18:48)
Continuity mistake: Ms. Perfect: The red strings attached to Lila's table and chair are only there as Lila is getting pranked; they are not visible in any other shot of the table. Also, when Rhonda pulls the string attached to the table, the string attached to the chair isn't there. (00:18:32)
Continuity mistake: Ms. Perfect: When the flap on Lila's table falls down, her lunch bag falls over. When the tray of spinach and fish falls on her, it changes position. (00:18:37)
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.