More on lateral connections is coming, but I got sidetracked by a thought this weekend. Someone on twitter was talking about bringing "Roleplay" oriented mechanics, like Aspects, into 4e, but was worried that getting his players to RP would be like pulling teeth. I sympathize with this a great deal, so I just wanted to throw out a few observations about systems out there and what purposes they serve, in hopes of finding a toolset that might appeal to recalcitrant players.
First and foremost, if you're going to do anything like this in 4e, you need to retool action points. As they currently exist, the limits on spending them make them poor rewards, so you want something that makes them easier to use more often. There are lots of cool ideas for this, but I favor using the model introduced in 3.x Eberron - each AP is a 1d6 that you can add to any roll after the fact. You can limit it to attack and skill rolls, or you can expand it to things like damage and saves - totally a function of taste. The only real limiter I would suggest is that they be a one shot thing - you can't keep spending them 1 at a time until you succeed. Just spend however many as you like, roll them, and move forward (and if you really want, put a cap of, say, 5 rolled at once).
Making a change like that make it much easier to hand out AP rewards for whatever you want more of in your game. In this conversation it's broadly "roleplaying" but it could be different or more specific. If you want to reward playing to alignment or engaging NPCs or even just following the plot, then you can do that. Just try to have a clear sense of what you're rewarding.
(Plus, as a bonus, you can get some cool colored d6's and physically hand them out as the action points, rather than using chips or tokens.)
Anyway, given that, I would strongly suggest against using Aspects in straight 4e, if only because they can cause too much whiplash. Invocations aren't the problem, but compels can be a sticky wicket, especially since they can seem to be a tool for GM fiat or bullying. Some groups take to the idea easily, but don't rely on that, since it's very much a taste thing. You're much better off with a less fuzzy mechanic.
This is one of the smart things about Leverage's distinctions. For the unfamiliar, they either grant a d8 bonus or a d4 penalty and grant a plot point, which is structurally aspect-like. The big difference is that it is totally up to the player whether something helps or hurts. The GM might quibble about whether it applies (usually resolved by the player incorporating it into his narration more fully) but the player is choosing to take the penalty himself.
This is hard to map directly onto 4e as there's no good standard model for penalties, but it's still useful as an illustration - things that players might be uncomfortable with the GM imposing on them, they are often more than willing to do themselves if you give them the chance. To this end, it's not unreasonable to put out _offers_ of plot points in return for bad or dramatic choices, nor is it unreasonable to reward players with PP when they do awesome things, but they will balk if you start telling them what they MUST do.
That said, some players still aren't happy with the GM having his power, and one other option is to move the reward mechanism to the table at large. The most common model of this is "Fan Mail" (from Primetime Adventures) , where players give points to each other when they do awesome things. Generally, this requires some sort of method to keep the points straight, such as giving each player a budget, or putting a common bowl in the center and letting people pay out of that. That may sound simple on the surface of it, but since we're assuming worst case here, you want to have some reason why players wouldn't just optimally distribute points to each other (even though that's pretty lame). One option, for example, is to have them grant them out of a common bowl, which the GM replenishes occasionally, with replenishment based on how many points remain, or how the points were distributed. In this case, you're trying to incentivise using the points as intended, but if your players REALLY won't, then you're better off falling back on a simple reward model.
Alternately, you could use the trick that Swashbucklers of the Seven Skies uses. Players start the game with a small number of points, which they can use for bonuses, or they can give to other players when the other player does something awesome. If the GM agrees it was awesome (which he usually does) then the GM can match that gifted point with one of his own. That is the only way new point get added to the economy, so it creates a curious situation where generosity is the best way to reward the group.
Anyway, my general advice would be this: Get players used to the idea of d6 action points as rewards before you do anything weird with them. Give them out as reward for skill challenges or cool scenes. Get the idea that they're rewards into people's heads. Once you've done that, start being more explicit about what they're rewards for. Tie them to specific things, like milestones or quests, but also give them out when a player makes the table laugh, or does something awesome. If they get comfortable with this, then things like fanmail or specific incentives using action points as rewards will not be much of a stretch. If they stay uncomfortable with this, then you know it's not for your group. If they call it metagaming, then they need to spend less time on the Internet.
But the bottom line is that introducing in-game rewards (mechanical bonuses) for roleplay is, for many players, a non-intuitive leap. They're different things, and the difference can be jarring. Far better to ease them into it and see if it works than it is to just throw them into the deep end and hope they swim.