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.
Arnold Visits Arnie / Chocolate Boy - S5-E12
Continuity mistake: Arnold Visits Arnie: When Arnold walks out of the movie theatre, he walks into Hilda and they fall over. In the next shot, they turn 90° counterclockwise. (00:06:45)
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.