These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
In the sequel - no, they weren't really going to kiss, but yeah...
It didn't help when the sand in the hourglass was suffocating Jedidiah, and he was trying to tell Octavius about how their relationship progressed "from enemies to friends and some stuff that will make you cry." Subtle.
Steve Coogan (who plays Octavious): There was a certain kind of subtext, what those of a discerning view might read as a subtle homoerotic subtext. If those people read that into it I certainly wouldn't argue with it... Yes, Octavius has a certain fascination with Jedediah because, of course, he wouldn't meet people as irreverent as that in the world of the Roman Empire, I think people were a bit more formal in their behaviour, so that slightly gauche, throwaway attitude that goes with being a cowboy fascinates Octavius, and he finds it quite alluring.
Then in the third film, when the tablet is corroding and the exhibits are dying, Jedidian and Octavius attempt to die whilst holding hands.
Joey Motorola, the helpful sailor who Amelia and Larry run into in the picture of V-J Day in Times Square; after star turns in Fanboys, Tropic Thunder, and She's Out of My League, you probably know who Jay Baruchel is by now.
Strangled by the Red String: Larry and Amelia. Amelia screwed around with most of the other exhibits while Jedidiah's life was at stake while Larry looked like an idiot in comparison and everyone around the complex just said that they were a cute couple.
Which is even weirder when you consider that Amelia is a mannequin
The second sequel Secret of the Tomb provides examples of:
Critical Research Failure: Unlike the Museum of Natural History in New York, the British Museum in London is solely confined to human history - mostly ancient cultures like the Romans and Egyptians - and has no reason to feature any dinosaur skeletons; they're all in the Natural History Museum.
They also don't have a medieval hallway, or a model of Sir Lancelot - who, it must be repeated, is fictional.
Harsher in Hindsight: Teddy being among the New York exhibits dying near the end foreshadows Robin Willams' untimely death. Not only that, Teddy losing the ability to properly move himself (due to his body becoming wax again), is eerily similar to Robin's diagnosis of Parkinson's disease (which he hadn't disclosed to the public, but was likely aware of during filming).
Heartwarming In Hindsight: Teddy Roosevelt saying goodbye to Larry is lent a ton of extra poignancy from being Robin Williams' last onscreen appearance.
Nightmare Fuel: The Roman Statues shambling around are quite frightening as the scene seems to have been taken straight out of a zombie movie with how they are missing limbs and stumbling about. So is Akhmenrah rapidly reverting into an undead human-mummy-zombie hybrid near the end.