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)

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
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)

Gerald's Game / Fishing Trip - S5-E15
Continuity mistake: Gerald's Game: When Arnold asks Gerald if he was in the alley near Dr. Steiglitz's office, there is nothing in the bottom shelf of Gerald's locker. When Gerald puts his book "The King Rules" in his locker, some books appear in the bottom shelf. (00:03:34)
Gerald's Game / Fishing Trip - S5-E15
Continuity mistake: Gerald's Game: When Arnold asks Gerald if he was in the alley near Dr. Steiglitz's office, Gerald is holding three books, with a purple book on top, and a green book on the bottom. Right before he drops them, the two books have switched places, and the purple book changes to blue. (00:03:24)

Summer Love (a.k.a. Beach Story) - S5-E9
Continuity mistake: In the scene at the end where "Babewatch" is being filmed, when Arnold drowns and the lifeguards save him, he is wearing his plaid shorts. A shot later, he is wearing his blue swim shorts. (00:22:34)

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 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: 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
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 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)

Stuck in a Tree / Rhonda Goes Broke - S5-E10
Continuity mistake: Stuck in a Tree: When the fire truck shows up at the end, in Arnold's close-up, his sleeves are drastically shorter than usual. (00:10:29)

Summer Love (a.k.a. Beach Story) - S5-E9
Continuity mistake: When the seagulls start flying above Arnold and Summer, they are both holding hands. In the next shot, they're not. (00:11:26)
Summer Love (a.k.a. Beach Story) - S5-E9
Continuity mistake: When Helga sprinkles bread crumbs around Arnold and Summer, six seagulls come and fly above them. In the next shot, the shadows of the seagulls are visible, but there are only two seagull shadows. Then when both look up at them, there are only five seagulls flying above them instead of six. (00:11:26)
Summer Love (a.k.a. Beach Story) - S5-E9
Continuity mistake: When Arnold talks to Helga after overhearing her, he tells her that he heard everything she said. As Helga says, "You did?", the lifeguard stand that was behind her suddenly isn't there. Then when Arnold and Summer walk away from her, they are suddenly a lot further away from the lifeguard stand than they were before. (00:11:47 - 00:12:12)

Summer Love (a.k.a. Beach Story) - S5-E9
Continuity mistake: When Arnold walks up to Helga after overhearing her, a surfboard suddenly appears behind Helga, which wasn't there before. A few shots later, it disappears. (00:11:42 - 00:12:07)
Monkeyman! / Buses, Bikes and Subways - S5-E1
Continuity mistake: Monkeyman!: When Sid tells the kids that Gerald should tell the legend of Monkeyman, Arnold is squinting. In the next shot, he's not. (00:01:41)
Helga's Masquerade / Mr. Green Runs - S5-E2
Continuity mistake: Helga's Masquerade: When Arnold compliments Lila's bows, she says, "In fact, I'm certain I wear them just, every old day." Ironically, her right bow disappears mid-shot, and it remains missing in the following shot. It comes back shortly after. (00:01:50)

Helga's Locket / Sid and Germs - S5-E7
Continuity mistake: When Sid decides to be a slob again, he picks up his frog and you can see that he has gloves on. When the following shot shows a close-up of the frog in Sid's hand, the hand holding the frog does not have gloves on.

Parents Day - S5-E6
Continuity mistake: In the tricycle section of the last event, the chinpiece of Helga's helmet keeps switching colors.
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.