In "The Busasaurus," Ms. Frizzle says that Tyrannosaurus Rex was the biggest meat-eater of all time. Too bad the discovery of the slightly larger Giganotosaurus was published in the same year the episode aired. In the same episode, Troodon is portrayed with scales rather than feathers.
Weirdly, "Gets Eaten" has Ms. Frizzle state that all food chains begin with plants, which had been a discredited fact since the discovery of hydrothermal vents in 1977, seventeen years before the episode aired. Even weirder, this error is pointed out in the phone segment, so it's not carelessness. The fictional producer's justification for excluding hydrothermal vents creatures is "Yeah, but they're weird."
A slightly better explanation for why they didn't include that in the show was that the majority of food chains begin with plants... and it's better to introduce children with a solid foundation of patterns before going into depth about all the exceptions.
Technology Marches On: As with most things of this nature, the computer episode went out of date the moment it aired. The fact that the computer has a "gajillion gigabyte hard drive" (something we don't even have yet) AND still has a floppy disk.
Part of the reason we don't have "Gajillion" gigabyte hard drives might be because... well... "Gajillion," is not a number. We do have computers and networks capable of working on Yottabyte levels (10^24 bytes).
In "Holiday Special," the whole plot revolves around an item being lost while the kids are sorting the school's recycling. As recently as 2007, many modern recycling plants no longer require manually-sorted inputs ("single stream recycling," a.k.a. one big bin for it all).