The Take Your Time event is completely justified at the end, especially how you arrive just in time: you have the Chronoskimmer, meaning you can take all the time you want and still appear at just the right moment.
Maybe Mediva wasn't as stupid as we thought in the 11th century - her notes are actually hidden amidst a shelf (full of paper) in the darkness (where you can't see), and in the one room with a heater. Since she stumbled over it, she most likely tried to throw it in but missed, and the guard picked it up before she could burn it.
Same thing could be said with Sir VILE in Egypt; one of the scraps was near a torch so he was trying to burn it. Why didn't he burn it? Hatshepshut or other guards came in - so he threw it or dropped it so he could get the heck out of there.
Belljar hides two of his fragments in the sewer and water pipes respectively - so he did try to destroy them.
So why does Carmen tell General Mayhem to hide in, of all things, the Bayou Tapestry? Presumably, Mayhem and Carmen were banking on the siege still going on - thus the room wouldn't be as crowded and they could use the chaos to sneak around.
Additionally, he wasn't hiding behind the Bayou tapestry - he was hiding in the room with it. The Bayou tapestry was a meeting point. When the siege was broken, he climbed up and hid behind the Bayou tapestry.
Some of the hiding places are actually plausible. Behind a secret panel, inside a small coal mine, under a tablecloth that extends to the ground, inside a bag attached to a llama, under a trap door...
Why doesn't the Universal Translator work in 1808? The language the Shoshoni spoke is dead.
They could have gone back to when it was still alive and recorded it, though. Then again, if ACME does so then they might inadvertently change the timeline of human history.
The game was actually right to depict Leonardo da Vinci talking to The Mona Lisa as a real person as mentioned in the trivia tab. But Da Vinci calls her "Mona". Meaning he's essentially saying "Madam".