The Gorgonops and the Rhinesuchus are only known from South Africa, yet in Clash of Titans, they are portrayed living with Scutosaurus, which was only found in Siberia. However, the gorgonopsid featured in the program was more likely an Inostrancevia, as it lived at the same time and place as Scutosaurus. Meanwhile, Rhinesuchus is also from South Africa. Although it is named, in the episode, as a labyrinthodont, a rather wide nomination that has been traditionally used to describe the more primitive amphibian or amphibian-like tetrapodomorphs that existed back then, including ichthyostegalians, temnospondyls, etc. The term labyrinthodont has since been disused, as it is ultimately nearly synonymous with the Stegocephalia clade as a whole, and conveniently removes amniotes, lissamphibians, and lepospondyls out of its definition. A more accurate replacement for it could be Konzhukovia, which lived in Russia at the same time the first part of the episode was set in and was a labyrinthodont just like Rhinesuchus.
It is possible that gorgonopsids had hair. However, correlations with the MSX2, a gene that is believed to be correlated with the manifestation of the parietal foramen and the distribution of hair in mammals, has been used to determine which extinct synapsids might have been covered in hair. According to studies done in regards to the manifestation of this gene, the mutations that activate the formation of parietal foramen, may be accompanied by the loss of extensive hair distribution, and that correlation has been made in extinct synapsids. Gorgonopsids, therocephalians, and non-probainognathian cynodonts (which include Thrinaxodon and cynognathians) had parietal foramen, suggesting they didn't have an extensive hairy integument.
Euparkeria is not an ancestor of the dinosaurs due to it being more basal than the crocodilian-dinosaur split. Probably the most likely ancestor of the dinosaurs at the time would be a basal dinosauromorph, likely quadrupedal.
The therocephalians featured in the episode, Euchambersia, would already be extinct 248,000,000 BCE. They lived from 256,000,000 to 252,000,000 BCE A possible replacement would be Moschorhinus, which survived into the Early Triassic.
Euparkeria, Euchambersia and Proterosuchus never lived in Antarctica, but instead in South Africa, which was, nevertheless, geographically close to Antarctica.
Proterosuchus was not the ancestor of crocodilians due to it being more basal than the crocodilian-dinosaur split.