In the scene where Zaius returns home and tells his servant he is going to read for a while, he is wearing his boots. When the scene cuts and he walks into his study, he is wearing the costume which has the "ape feet" with the big toe out on the side.
The events of Conquest of the Planet of the Apes take place in, "North America 1991." While the city is not identified, the events of "Battle," Beneath," and PotA indicate that it is NY. However, Virdon and Burke discover a book that shows New York still standing in the year 2503, 512 years after the city's downfall. Apparently this series built off of Cornelius' rendition of the apes having been slaves for centuries before their revolt, recited on "Escape From the Planet of the Apes" (1971).
They show Earth time as 1980 on opening credits but it was 1973 that two talking apes arrived through time from the year 3955 and became world famous so the astronauts should not of been surprised to find talking apes. This series seems to take place in an alternate time line.
The ape child has a pet dog but they were all culled over 500 years earlier.
In the first chapter, when the human prisoners are taken to their cell, they walk with their hands behind their backs as if they were tied. But when they enter the cell, they simply open their arms... they never had their hands tied.
Although it was mentioned that dogs and cats were wiped out in a plague in Escape from the Planet of the Apes (1971) and Conquest of the Planet of the Apes (1972), the young chimpanzee boy Arno and his Great Dane chase Farrow in the first scene.
Farrow states that apes are much smarter than man, yet he easily deceives an ape to go on a wild goose chase after the two fugitive humans. (Note: One of this series' main premises is that the humans are kept "beaten down" psychologically by the apes, keeping them uneducated and ignorant; the humans only being taught that they're inferior to the apes, despite the fact - as Zira had pointed out in the original movies - the gorillas are the more intellectually inferior race).