When the girls are overlooking the river from outside the Globe theater, watching Lord Pomfrey escaping in his launch, Celia licks her finger and holds it up (to determine wind speed/direction) but when they steal Drakes ship and it's moving down the river, none of the sails are unfurled.
When the girls are at the school looking for the ring, the headmaster goes into his office and the painting on the wall is in perfect condition while all the girls rush out of the office secretly. Then, when they are in the van heading back to St. Trinian's, it shows that they ripped the painting to get the ring.
Notice Miss Fritton throw a dart at Twaites picture, but in the previous scene she picks up a letter opener to throw.
Kelly states that she now works for MI7 which was a real section of the British military intelligence but is no defunct and even when it was still in action it was concerned will propaganda and censorship which is a weird one for her to be involved in.
The clothes Lord Pomfrey is wearing at the start of the are in the style of the mid to late 17th century. That section is supposed to take place in 1589, therefore the clothes and wig are completely wrong for the time period.
At the very beginning of the film it states that it is 1589. Then shows a view of another ship through a telescope, the telescope wasn't invented until 1608 by Hans Lippershy.
The engraving on the ring supposedly shows the coordinates of the treasure according to currently used geographic coordinate system, which is based on a longitude of the Greenwich Meridian. It was only established first by Sir George Airy in 1851, much later than events depicted in the story of the treasure.
At the beginning of the film the sailors are heard singing "Fifteen men on a dead man's chest / Yo ho ho and a bottle of rum!" This is not a genuine sea shanty but was created by Robert Louis Stevenson for the novel "Treasure Island", published in 1883, so the sailors would not know it.