Good point! You’re totally right that carryover of events is a lot of mental heavy-lifting. I used to take extensive notes during sessions, or keep character diaries, but I’ve fallen out of that habit, and now it’s often a huge challenge for me to even remember the bare events of the previous session.
(My current Monsterhearts character has a character journal, but because it’s very much written in her voice, and because she cares about some things more than others, it’s not a great record of what happened in the previous session, especially if she has to interact with her crush at all…)
As I remember it, at the end of a session of Leverage, players are encouraged to recap one awesome thing that either they, or someone else did. Then you record on your “episode log” the episode title and a highlight moment for your character. So if your hacker character had to skydive in The Pencil Case Job, then four sessions later, during The Locked Clock Job, you can say “Oh, remember back when I had to skydive? I’m going to call on that experience now to add a d8 to my pool.”
If that’s right (and maybe it isn’t) it allowed the event to be recorded contemporaneously, and banked against future opportunity.