Heroic consequences are a third "pool" of consequences (in addition to the usual Physical and Mental), but one shared by the PCs instead of belonging to any of them individually. They represent, and give more significance to, their failures -- stuff like property damage, civilian casualties, falling reputations, and the like. Think of them like campaign aspects, but... y'know, consequences instead.
When a PC fails to defend against an attack, the player can choose to reduce the incoming stress (because we're using that, at least for the time being) with either one of his own consequences, or a Heroic consequence. The latter means that the PC gets the reduce the stress without suffering himself, but something bad happens to the environment around him. An innocent bystander could get knocked out, a car could be crushed, an office building could burst into flames, the public could turn against the PCs -- whatever.
For example, Roborilla, the supervillainous robotic gorilla, throws a compact car at the Blue Knight, who throws up one of his trademark blue force fields to stop it. But he's too late -- his defense roll fails by 4. The Blue Knight has three choices:
- He can take 4 Health stress, a result of dodging out of the way in the nick of time.
- He can take a Physical consequence, like "Knocked Off Balance" or "Cracked Ribs." The car's hit him, and he's worse off for it.
- He can reduce that 4 Health stress with a Heroic consequence, like "Smashed Storefront" or "Civilian Trapped Under Car." The car's missed him, but it's caused some trouble elsewhere in the scene.
To recap: Minor consequences go away at the end of a scene, Moderate consequences can only be removed with a Great skill check, and Severe consequences only go away at the end of the story -- but they change an aspect when they do.
So going back to the example of Roborilla and the Blue Knight, "Smashed Storefront" is a Minor consequence. It's not really something the PCs are going to be expected to set right. We can assume that it's mundane enough that someone else will take care of it later. However, it still represents collateral damage, and the PCs are still indirectly responsible (Roborilla was throwing that car at the Blue Knight, after all), so it's fair game for a Heroic consequence.
"Civilian Trapped Under Car," though, is best as a Moderate consequence. It's a clear and present dilemma for the PCs to solve, either during the scene or right after (after that, for a consequence like that, it's too late -- the story's moved on to the next scene). If they don't solve it, the consequence sticks around -- and the next time they might want to take a Moderate Heroic consequence, maybe they'll have to take a Severe consequence instead, maybe something to do with the fact that they just left some dude to be slowly crushed under a car. "Public Turns on the Hero League," say. At the end of the story, one of the campaign aspects changes to reflect the public's similarly changing attitudes towards the PCs. For example, "Hero League to the Rescue!" could become "Misunderstood Heroes."
How late is too late to deal with a Moderate consequence? Right now it's a matter of common sense, I think. If a guy's trapped under a car, he'll need immediate assistance. I'd say that if you don't take care of it before the next scene, you missed your chance to clear that consequence slot. If your reputation takes damage, though, that's more of a long-term issue, and something you should be able to try to remedy almost anytime. Of course, it's also more involved than a single civilian under a car -- you need to call a press conference, get yourself on TV, or something along those lines. It's all very Marvel.
Here's another one: Ultra-Violence drops a hostage from the top of a 10-story building. If the PC fails to save the hostage (by flying up and catching him, using TK to get him safely to the ground, cushioning his fall with an awning or something, etc.), he can take a personal consequence, indicating that the hostage actually was saved, but the rescue took a toll on the PC. It can be something as minor as being winded or as significant as almost killing himself in the process of saving an innocent life. Alternately, if the PC goes for a Heroic consequence instead, that indicates that the guy actually was hurt, if not killed, in the fall. He can walk away from a Minor Heroic consequence, a Moderate Heroic consequence will probably require medical attention (or, if the consequence involves the PCs' reputation instead, a Great Art or Rapport effort later on), and a Severe consequence will likely mean the hostage fell to his death.
The upshot is that these Heroic consequences can help drive the narrative. "Building On Fire"? Someone should probably take the time to put that fire out, possibly in the midst of combat if they want to free up that consequence slot for use later in the scene. Press conference? Failing to get the press on your side may be a Moderate Mental consequence ("Frustrated!") or a Moderate Heroic consequence ("Front-Page Hatchet Job") -- and if the latter, you probably want to get that cleared up, before your poor public image bites you in the ass later (i.e., you only get one Moderate Heroic consequence, so if you don't clear it, you may find yourself stuck with a Severe Heroic consequence later on).
Lastly, Heroic consequences can be tagged or compelled like any other consequence, as long as it makes sense. "Smashed Storefront" might not make for an easy compel, but "Civilian Trapped Under Car" sure does. A supervillain attempting to cow an auditorium full of would-be victims is going to be able to tag your "Distrusted by the Public" Heroic consequence as part of his Art roll, because these poor people just don't have any confidence that their "heroes" are going to save them.