At different times, the sidecar is on the left or right side of Nanny's motorcycle.
Vincent's teeth can be seen as different sizes throughout the movie showing that scenes were not filmed in order.
During the scene where the syrup is in the drawers in the shop, Isabel can be seen closing one of the drawers twice.
Farmer Macreadie arrives at noon to pick up the piglets. Right after he leaves, when the sun should still be high in the sky, it is just over the trees on the other side of the field.
When Megs is reading the letter from the boys who've gone to London the paper changes size; when viewed facing Megs it is a large sheet with an obvious fold but, when viewed so we can see the writing it has been cut off at the fold.
During the motorcycle trip through London, none of the vehicles that Nanny McPhee drives past have blackout covers on headlamps. These were mandatory in England during WWII.
When the two boys are being escorted through the War Office, a WAAF plotter can be seen in the foreground. The rank on the arm is that of a Lance Corporal - a rank that didn't exist in that Service.
Nanny McPhee calls the red-coated soldier "Sergeant Jeffreys". Not only does he lack sergeant's stripes on the sleeves of his tunic, but he also has a crown on his epaulettes, indicating the rank of major.
As a guard at the War Office, Sergeant Jeffreys should be wearing battle dress, not ceremonial dress. He would not escort visitors into the building but would pass them onto another serviceman. Even if he did accompany the visitors, he would not march in carrying his rifle.
Sergeant Jeffreys' tunic is far too long, being part-way between the proper tunic length and that of a great coat.
The first Nanny McPhee was set in the late 1800s to early 1900s, so baby Agatha would only be in her late 30s to mid 40s during WWII in England.
Farmer MacReadie says he heard of a pig which played Scrabble, but the game was known as Criss-Crosswords until 1948.
The War Office is guarded by a black man in the traditional uniform of the regiments of Foot Guards, who guard the British Monarch - red tunic, large bearskin hat. The single spacing of his buttons indicate that he is a member of the First Regiment of Foot Guards (aka The Grenadier Guards). The first black member of the Foot Guards joined the Grenadier Guards in 1985.
Mr. Docherty wears the uniform of the Civil Defence Corps. This unit was formed in 1949, long after the WW2 setting for this film. With his white "W" helmet, he should have worn an ARP uniform.