When Stubbins is squeezing the fruit of the Cure Tree into Queen Victoria's mouth, the first drop falls into an open mouth. The second drop shows falling onto closed lips.
The dandruff on Stubbins's jumper when knocking on the Manor's door.
When they arrive at Buckingham Palace (they actually arrive at Blenheim Palace), they are greeted by Guardsmen. The red plume indicates that they are Coldstream guards. However, the plume is on the wrong side of the bearskin, it should be on the right, and the buttons are wrong, they should be in pairs, one vertical line of buttons.
The pellet is supposed to be removed from the squirrel's heart, and Dolittle just falls into his chair without suturing or repairing any tissue, flesh, skin or whatsoever right after removing the pellet and throwing it in a container (very common Hollywood depiction of a surgical procedure).
The pellet removed from the squirrel at the start of the film is clean. It should have had blood residue on it.
When going to see the Queen, the animals and Rose claim they are going to Buckingham Palace. Yet, they arrive to Blenheim Palace, which is not only not a royal palace, but also not remotely similar in either location or architecture to Buckingham Palace.
The pellet is supposed to be lodged in the squirrel's heart, which would have killed it instantly.
The plaque on Dr. Dolittle's gates invites people to "Inquire Within". In British English, the sign should say "Enquire Within".
One of the Queen's royal guard mentions talking to ladybugs. In England, these insects are called ladybirds.
Dr Dolittle knows so many animal languages but fails to pronounce Monterverde in proper Spanish: Mon-Tay-Bair-Day and not Mon-Tay-Vair-Dee.
Müdfly is very well educated but fails to pronounce the French word Madeleine properly: Mad-Uh-Lane and not Mad-Uh-Line.