Big Lipped Alligator Moment: "CHEESE GIRL!!!" Subverted in that in the Adventure Mode in Buried in Time, this was a helpful item for getting to a space station. Double Subverted in that, unlike most examples of this trope never being mentioned again, this was briefly shown again at one point in the alien spacecraft, no matter what mode you're playing.
The third game allows you to do a lot more with the people and scenery, including incredibly elaborate changes to Shangri-la, which would seem to violate the rules of the last two games. Until, of course, you realize all three will be destroyed in 24hrs and have no effect on history... (See Fridge Horror).
The TSA put a lot of futuristic equipment in the prehistoric time zone in Pegasus Prime, but, as your AI Biochip explains, that too will be destroyed when the nearby volcano erupts, as the island everything is on is geologically unstable. This explanation also works for the Turbo version.
Fridge Horror: You meet a lot of nice, friendly, funny, and endearing characters while time-travelling in the third game. Every single one of them will be die horribly in twenty-four hours' time when the warring aliens destroy the three ancient civilisations. Yes, even that cute kid in El Dorado.
Fridge Logic: How did Michelle return to her own time after she abandons her suit in Atlantis?
Possibly through use of the suit's secondary features. In the 2nd game, in the intro, Future!Gage is found and apprehended by a fellow suited time travel agent. He at the time does not have one. The same beam he uses on Gage is equipped on the suit. She conceivable could have used this to boot herself to the time you find her in.
Or maybe kit bashed something to activate the recall function. Or maybe there was only enough power to return her or the suit.
In Pegasus Prime, why is the exit of the circular desk in the TSA's command center not facing the door, or likewise, why was the Pegasus device built in a way that it doesn't face the turbolift from the Ready Room? You'd think a quick path to the Pegasus in a hurry would be necessary in an emergency like the temporal distortions. And if that wasn't weird enough, this is a change that was implemented in Pegasus Prime over Turbo.
There's also the very first words that Arthur says to you when you make it to the Amarax station for the first time. Even when he takes off the ghostly filter when admitting "That always seemed to work in Scooby-Doo," his agitated sentences after that still sound unsettling. The spacey music in the background does not help at all.
"GET! OFF! MY! STATION!"
Hilarious in Hindsight: The acronym for the Temporal Security Agency has a double meaning with the Transport Security Administration.
Narm: The acting in Turbo isn't that great, except for Elliot Sinclair. Geno Andrews did several voices, but spoke in a rather slow fashion, including the interface overview.
Most of the acting in Pegasus Prime is fair, though you won't encounter much unless you want a game over. But special mention goes to that Doc Brown-esque scientist who sees you when you try to leave Dr. Sinclair's office. Having Sinclair's antique gun on you causes an even sillier scene.
Scientist: "*gasp* You're not Elliot! Security! Security! Don't shoot the man with the glasses!"
The two guards playing Rock Paper Scissors behind a door in the Mars Colony start arguing on who should capture you if you open the door.
Nightmare Fuel: Lots of it, particularly the underground section of Mars (scary ambient music, big scary robot that kills you in a scary way, the Shield Generator, with more scary background noise, that skeletonizes you if you take too long solving the puzzle, and the Maze with the music that slows down as your oxygen decreases, and finally fades to heavy breathing and heartbeats), and Sinclair's lab, where you get shot with a dart and are slowly dying, while creepy/sad music is playing.
Most Annoying Sound: The alert in NORAD VI of sleeping gas in the base's vents. This goes off for almost the ENTIRE TIME ZONE! At least Pegasus Prime tones it down a bit.
The Computer Is a Cheating Bastard: The 2014 version of Pegasus Prime does a very sneaky trick during the shuttle pursuit quick-time scene. Even though Ares' ship banks left to enter the launch tube at the end, you have to go right, or else you have to start from the beginning again.
Scrappy Mechanic: In both the original game and Buried in Time, you always start in the same location when traveling to a specific time period (mainly to prevent the game from becoming unwinnable). This isn't much of a problem in Turbo and Buried in Time, as there isn't a ton of required backtracking outside of a few items. Pegasus Prime, on the other hand, switches up item locations just enough to make this very annoying. You have to do a lot more jumping between time periods to get the required items, so you'll have to navigate the same areas and watch the same animations multiple times as you progress. Especially annoying with the Mars Colony, where you'll be forced to do the rather long mine tunnel segment more than once.
Fortunately, Legacy Of Time removed this mechanic, allowing you to lock in the location you last left a time zone from, so that you can come right back to it later.
Replacement Scrappy: One of Pegasus Prime's largest problems is the AI Biochip you're given at the start. It replaces not only the relatively benign text message window from Turbo, but also the woman in the TSA videos. The problem with this is that in-game, this version's warnings and such are much more harried, inconvenient at times, and sometimes fall into Captain Obvious territory, especially if you've already played Turbo.
Fortunately, pressing any movement key cuts off what she's saying mid-sentence. And an Easter Egg where a copy of Arthur can be found has controls to toggle both him and the other AI on or off.
Series Continuity Error: While Pegasus Prime did a good job connecting with the fleshed out storyline which Buried In Time kicked off following the original game, it still makes a couple of minor points look confusing and out of place.
The intro cutscene of the second game shows that Agent 5 kept the maintenance key from Mars, when in Pegasus Prime, there was no key available. Weirder still, this same intro goes unedited while tacked onto Prime's ending as a cliffhanger.
In Buried In Time, the Interactive News Network shows video footage of the original game.
Squick: In Turbo, hidden in a corner next to Elliot Sinclair's video log in the World Science Center is a viewer that shows the first stages of Bio Tech devices, in an endoscopic view of a rat's brain being worked on WAY up close.