The Mesothelae spider in the program was based on Megarachne, which during the show's production was thought to be the largest spider ever to live. However, as production was wrapping up, another specimen of Megarachne was discovered that led to the realization that it was actually a eurypterid, leading to the animal in the program being referred to as a speculative species of giant mesothelae spider (an actual group of extant spiders that existed back in the Carboniferous, but its members only vaguely resembled the one from the program and were nowhere near as large).
Proterogyrinus was not an amphibian, though it may have lived an amphibious lifestyle. It was possibly a reptiliomorph.
There is no evidence suggesting that Arthropleura had powerful jaws, given the fact that its mouthparts have never been preserved along with the rest of the animal.
Arthropleura is now known to be a true millipede rather than a distant relative of them.
Arthropleura's ability to rear up is purely speculative, and it might not have been possible in real life.
Petrolacosaurus is incorrectly shown evolving into the synapsid Edaphosaurus, when in fact, it was an early diapsid, and could therefore not have been the ancestor of any synapsids. The most basal synapsid, Protoclepsydrops, would have been a more suitable candidate. However Edaphosaurus were already present 300 million years ago, so their ancestors would still be Edaphosaurus.
The Dimetrodon hatchlings are shown with their back sails fully erect, when they probably wouldn't have grown them yet.
The skin texture of Edaphosaurus and Dimetrodon may be slightly off. It is hypothesized they had scutes on their skin, similar but different to the ones on crocodilians. It's possible they lacked the scales of lepidosaurian reptiles.
There is no evidence that Dimetrodon were cannibals, however, this is not impossible.
There is no evidence that Dimetrodon eggs would take 7 months to hatch, but we do not have any information on Dimetrodon reproduction whatsoever, so any reconstruction of their reproductive habits will always be speculative until potential future discoveries prove otherwise.
Dimetrodon is depicted as living in a desert-like environment, when in fact, Dimetrodon is known to have lived in a swamp-like environment. However, it is still possible that some populations lived in slightly more arid environments than the average.
The tops of some Dimetrodon's neural spines could have been exposed bone rather than covered with a full sail, though that is debated.
In the programme, Dimetrodon and Edaphosaurus are described as "mammal-like reptiles". However, they were not reptiles, as synapsids form a distinct clade within Amniota, which also contains "reptiles".