It is not true to say, as the film claims, that before Louis Wain cats were not kept as pets in Britain. Many famous people were open about having cats as pets throughout the 19th century and before. Notably Edward Lear, Emily Brontë, Horace Walpole, Florence Nightingale, Robert Southey and Queen Victoria to name but a few.
Peter is not the same cat as he was as a kitten.
His nose as an older cat is black, as a kitten it is pink.
Cats markings do not change.
When Louis and Emily hear the kitten, they take a long walk to the edge of the garden to find the kitten meowing. There is no way they could've heard that kittens meow from that distance.
When Mr. Wain first arrives in New York, as he walks along a city street. The year shown on the screen is 1907. As he walks down the street, he is passed by several horse drawn carriage and then an automobile of early 1900 vintage. Next, another in car passes which is from the post 1915-1925 era, later than the timeframe depicted.
Wain is shown tuning a radio with a dial and receiving voice transmissions in 1907. No such radio existed for another 15 years.
A blue point birman cat is shown in a couple of scenes. Birmans weren't imported into Britain until the 1960s and only officially recognised in Britain in 1966.
When Louis visits New York in 1907 there are neon signs on buildings which were not invented until late 1910.