When Queen Marie is with Cromwell in his room, she says he rescued her from Hampton Court Maze. The Maze wasn't planted until 1689-95, more than 140 years after the film is set. However, the present-day maze was based on an earlier one from Cardinal Wolsey's time, so Queen Marie and Cromwell could have known of the old maze, not the one that's there today.
At the end of the film, Henry VIII asks the name of a maid. If she is Catherine Howard, as she says, that dates Carry on Henry VIII (1971) to some time between the 9 July 1540 (when Henry divorced Anne of Cleves) and the 28 July 1540 (when he married Catherine Howard). If that's true, where are the king's children? Mary, having been born in 1516, would have been aged 24; Elizabeth, having been born in 1533, would have been aged 7; Edward, having been born in 1537, would have been aged 3.
Sir Roger de Lodgerley (Charles Hawtrey) is wearing NHS (National Health Service) issue spectacles which were not introduced until 1948.
Towards the end of the film, when Lord Hampton and his men are preparing to rescue Queen Marie from the Tower, the gunpowder fuse used to blow up the gates goes out. When it does, you can see the line of gunpowder is about an inch too short and does not reach the barrel, meaning it was meant to go out in the first place.
When Henry VIII is chased out of the barn by the buxom lasses father you can clearly see it is a double not Sid James who is doing the running.
Queen Marie states that garlic prevents germs (which is a goof in itself) but germs were not discovered until late 19th century.
Guy Fawkes was not born until 23 years after Henry VIII died.
Sir Roger is tortured with an Iron Maiden. However, the earliest known Maiden does not appear until 1793, and was probably not a genuine torture implement, but a fictional 'medieval' device designed to shock and fascinate paying visitors to an exhibition.
At one point, Henry and his courtiers are seen out riding in Windsor Great Park. However, many of the features of the Park and Windsor Castle in shot were not built until the mid-17th to early 19th centuries; for example, the Long Walk along which they are riding was constructed by Charles II in the 1660s, the trees were planted by William III in the 1680s, whilst the current south range of Windsor Castle's Upper Ward, and the upper story of the Castle's Round Tower, were built by George IV in the 1820s.
King Francis of France mentions that his wife had "caught her neck on the guillotine". In France the execution device was not called a guillotine until much later, at the end of the 18th century.
At the early banquet, it is suggested the king " have a cup of tea and a bun" in his room. Tea was not introduced to England for another 120 years.