I've been talked into running a 1-shot of Continuum at GenCon for some friends.  Now, while I get the setting, I'm drawing blanks on what to actually give the PCs to do.  If it wasn't a 1 off I'd give the players some leeway and sandbox it more.  With only 3-4 hours though, and pregen characters, I think something focused will work better.  Right now I'm leaning toward some sort of murder mystery.

Anyone have any ideas for/experience with what would make a good session for a game with lots of (pretty easy to do) time travel of the Bill and Ted "in the future we can go and leave a gun behind the trash can in the past so we have it now" variety?

Not being familiar with the Continuum universe, you could do something like a heist. They have to get to certain physical areas of the building, avoiding security, then go back in time to a specific point to set up what they need at that location for the overall heist to work. Like this example: The PCs need to access the time lock on a vault that are going to rob, but it's only accessible during a short time period when the head of security is setting it up. They have to sneak into the building in present time, avoiding security, go back in time to when the security chief is there, get in, change the time lock so it will be open when they rob it, and then get back to present time. All while avoiding the chief so that they don't get discovered and the time lock is reset again.

Another might be to go in present time, find out who one of the guards who will be present are, then go back in time to sabotage his ability to get to work so that one of the PCs can "fill in" for him.

So, all you would need is a heist plan made up of maybe a half-dozen predetermined actions they need to take in certain areas of the site in order to set up the final act with the actual heist, using the individual specialties of the characters, with their overall success in the adventure relying on how well they do in each of them.

Black Ferret has the right idea; railroad the fuck out of it. I ran a session of Mutant Crawl Classics at Garycon, and it was far more stressful than any game I've ever run. 4 hours is barely enough time to introduce the characters and setup anything, so you pretty much need a MacGuffin, pregens, and a linear adventure. Just be upfront and let the players know their goal, no need to hide clues or anything. If they aren't dicks, they should take any plot hooks like a perch in a small pond and run with them.

More specifically, what's wrong with the idea you used? Maybe they have to leave a gun for someone to shoot Hitler, but their contact in the past got killed. Turns out it's another group of time travelers who are thwarting their plans. Something simple.

Continuum is super-duper complex.  I think maybe the most interesting thing about it is really the weird societies lost in time in the very distant past. These were further elaborated on in the sourcebook they release (whose name escapes me just now).

One shots definitely need pregens and an adventure where you can have beginning, middle and end happen in 4 hours with snacks and potty breaks. However, I somewhat disagree on the need for a railroad and a linear adventure. Those two certainly help achieve the goal, but you risk turning the game into a ride. Instead, focus on a tight situation that requires swift attention and then let the PCs loose to solve (or fail to solve) the problem.

I am heavily guilty of overplanning for one shots, but over the decades, I've gotten better at tighter focus. Like with dungeons. I know I can do max 10 "rooms" in 4 hours so my last adventure was 4 rooms on the first floor, 3 on the 2nd floor and 2 on the 3rd level down.

Yeah, I've got a few pregens already done.  With such a tight time limit I don't want to spend any of it having the 3 players do it themselves when we sit down.  If it was a more rules light game maybe.

The expansion book is Further Information: A Gamemaster's Treasury of Time.

Because of the complexities of time travel Continuum presents, I'm giving them all a few pieces of scrap paper to keep notes of their Yet (what they still have to go do in the future because of their actions in the Now).  I doubt much of that will come into play, at least the taking care of it part.  I do want them to get the feel of how important keeping track of that info is.

Right now, I'm thinking of doing something like having one of the PCs have a Gemini incident with an Elder self (a future version of themselves).  The Gemini just shows up on the PC's corner (home), bloody and beaten and amnesic.  Cue investigation as to how that happened.  This gives a nice definitive arc to play thought, but gives them a bunch of freedom to do it their way.