
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
Revealing mistake: Monkeyman!: When Arnold tells the kids that Monkeyman saved him, as he says, "He went after the two guys who were trying to mug me," he moves his right hand, and it's layered over Helga's hair. (00:01:25)
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)
Monkeyman! / Buses, Bikes and Subways - S5-E1
Audio problem: Monkeyman!: When Gerald begins to tell the legend of Monkeyman, as he says the word, "Monkeyman," it looks as if his mouth only says the word, "Man," and it never says the "N" sound at the end. (00:01:50)

The Aptitude Test / Oskar Gets a Job - S3-E9
Other mistake: Oskar Gets a Job: On the second day that Oskar forgets to do his job, Arnold reminds him that he has newspapers to deliver. After Oskar says, "You won't believe what happened," Arnold blinks, and his right eyelid is not colored in. (00:18:56)

The Aptitude Test / Oskar Gets a Job - S3-E9
Other mistake: Oskar Gets a Job: In the beginning of the episode, Arnold and Gerald overhear Oskar arguing with a man in his room. In the close-up of Arnold and Gerald as Oskar says, "You're a big man, aren't you?", Arnold's right eyelid is not colored in. (00:12:17)

Helga's Boyfriend / Crush on Teacher - S2-E14
Other mistake: Crush on Teacher: When Arnold and Gerald are walking to school and Arnold gets distracted by the birds and flowers, as he says, "Look at the flowers," his eyelids are not colored in. (00:14:37)

Helga's Boyfriend / Crush on Teacher - S2-E14
Other mistake: Crush on Teacher: When the kids are playing baseball and the baseball hits Arnold, as he says, "I'm fine, Miss Felter," his eyelids are not colored in. (00:13:02)

Revealing mistake: In Arnold's nightmare, when Bob points out that a stork is flying off their roof, his legs are incorrectly layered behind his cape. (00:12:50)
Grandpa's Packard / Phoebe's Little Problem - S5-E19
Audio problem: Phoebe's Little Problem: When Harold wets his pants at the end, Stinky can be heard saying, "Harold wet his pants," but in the shot, he is actually laughing. (00:11:39)

The High Life / Best Friends - S2-E10
Other mistake: Best Friends: When Arnold walks across the table during the fashion show, a small chunk of the spotlight vanishes mid-shot. (00:22:13)

The High Life / Best Friends - S2-E10
Other mistake: Best Friends: When Gerald is first revealed during the fashion show, the curtains are transparent. They are never transparent in any other shot. (00:22:26)

The High Life / Best Friends - S2-E10
Continuity mistake: Best Friends: During the fashion show, in the close-up of Arnold showing off the antennas on his costume, the curtains that he came out of are missing. They are also missing in the shot after Arnold tells Gerald, "Just smile and move, okay?" (00:22:22 - 00:22:50)

Runaway Float / Partners - S2-E20
Other mistake: Runaway Float: After Bob says, "Now this float has to scream 'beeper' at the top of its lungs!", as he walks away from Arnold and Helga, Joey has white skin, blonde hair, and an orange shirt. (00:06:31)
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)

The Beeper Queen / Oskar Can't Read? - S4-E4
Continuity mistake: Oskar Can't Read?: When Oskar comes home at the end, Ernie and Mr. Hyunh are standing on Arnold's left. As they walk inside the house, they are on Arnold's right. (00:22:36)

Arnold's Room / Helga vs. Big Patty - S3-E4
Other mistake: Helga vs. Big Patty: When Helga dreams about boxing Patty, as she steps back from her, she is standing in mid-air for about a second. (00:17:00)
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.