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)
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 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 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)
Part-Time Friends / Bio Square - S2-E19
Continuity mistake: Part-Time Friends: When Arnold and Gerald get part-time jobs at the flower shop, while Mrs. Vitello explains things to them, she asks if she's going too fast, and in the next close-up, Arnold's apron vanishes, then it reappears.
Runaway Float / Partners - S2-E20
Continuity mistake: Runaway Float: When Arnold first sees the beeper float, he says, "How can they control that thing?", and Gerald is sitting on the curb to the right of Arnold. In the next shot, Gerald is suddenly behind him. Arnold is also a lot further away from the curb than he originally was. (00:08:16)
Runaway Float / Partners - S2-E20
Continuity mistake: Runaway Float: The big beeper float constantly changes appearance during the parade. Some examples: The sign saying "Let's Go Downtown" on the front changes to "Let' Go Downtown" in one shot. The sign saying "Let's Go Downtown" on the back is missing in one shot. The orange base is sometimes blue. The blue city design around the base sometimes isn't there, and it even changes colour. (00:08:17)
Runaway Float / Partners - S2-E20
Continuity mistake: Runaway Float: When the beeper float first starts to speed out of control, in one of the shots, Helga is wearing her regular outfit, not her beeper costume. On top of that, the kids on the float are smiling and waving, not freaking out like they were before. (00:08:39)
Runaway Float / Partners - S2-E20
Continuity mistake: Runaway Float: When Arnold reaches the parade float on the bike, Iggy's shirt is incorrectly coloured green instead of purple. It's also green when the float rides past Mayor Dixie. (00:09:45)
Runaway Float / Partners - S2-E20
Continuity mistake: Runaway Float: When Arnold stands up on the bike before jumping onto the parade float, Eugene's hair disappears mid-shot. (00:10:11)
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.