Uncle Martin claims that Leonardo da Vinci invented the catapult. In fact the catapult was used in warfare by the ancient Greeks and Romans, centuries before da Vinici was born.
Brennan tells the guards who are guarding the Mona Lisa to lock Tim is the museum's anti-room for illegal entry into the museum. Short time later, the guards are outside the anti-room guarding Tim which means there is no-one guarding the Mona Lisa. Later Brennan tells the guards to accompany him to Tim and Martin's house, again leaving no-one guarding the Mona Lisa.
The second time Martin extends his antenna inside the museum, the man operating them is visible in the corner of the shot.
When Leonardo Da Vinci departs back to his own time, Martin sends him off with the French greeting, "Bon voyage!" But Leonardo is Italian, not French, and Italians do not speak French; especially not in Da VInci's era. In Italy, they say "Buon viaggio". Martin being a cultured martian who speaks several languages, knows history and has proper etiquette, so he would know the correct greeting, particularly since Martin had lived in that Italian era. So, it is in bad form for Martin to salute the painter with another country's greeting, where the French expression has not been adopted, like it has in the USA, Martin not being an American either.