I think I want them to be representative of the character's increasing mental/emotional stress. Stress that results from their disads. Not every time a disad comes up, but when the character fails to do the right thing (in their own eyes.) So Spiderman has "Loves MJ Watson." If he is so caught up in chasing a bad guy that he misses his anniversary dinner he gets a soap point. Of course, since this is Peter Parker he also has "With great power, etc." so if he lets the burglar get away (shades of Uncle Ben) he gets a soap point for that too. Poor Peter, always seems to be caught in a cleft stick.
What does that soap point actually do?
Well there's plain old mechanical penalties. The GM (maybe the player can call for it to be spent?) spends the soap point and Spidey takes a penalty that represents their distraction/loss of faith in self/whatever. Maybe the penalty could apply to a whole scene. A -1 penalty/soap point used that an be applied to OCV, DCV, or ECV.
Invoke a character's disad; meaning the chacter automatically fails a disad check or does the GM get to set up a scene in which the disad comes up? I'm leaning toward the former. Spidey has tracked the bad guy to a lair, the whole stinks of a trap. The GM invokes "With great power." Spidey knows it's a bad idea but he can't take the chance that the bad guy will get away and so goes into the obvious trap. At least he knows it's a trap, right?
Add something to a scene to heighten the stakes - something specific to the character and if possible to one of the invoked disads. Say, MJ, wondering why Peter is late for anniversary dinner, comes looking for him, only to get caught in the middle of Spidey/Scorpion battle.
Hmmmm, how about, I wanna call it Double or Nothing. The player can gamble soap point on another shot at the disad. If the player wins the soap point(s) is removed from play without being spent. If the GM wins they double the soap. Spidey from the above example is swinging along after Scorpion (I've retconned that burglar into Scorpion) and he goes past a billboard with MJ on it (she's still a model right? Doesn't matter, in this continuity she is.) Spidey is reminded of anniversary dinner and gets another chance to resist their "With great power" disad so as to not disappoint her. If they successfully resist the disad they can give up chasing Scorpion and go for dinner instead. No soap for missing dinner with MJ! If they fail to resist the disad and keep chasing Scorpion they gain 2 soap. Of course, as mentioned above, poor Spidey is in a cleft stick here because he still gains soap for failing to chase Scorpion. So unless there's different amounts of soap for these different actions (based on the strength (moderate, strong, or total)) of the disad. there's no point for the player to play double or nothing in this scenario. Hmmmm. This Double or Nothing thing clearly going to need some more thinking if it's going to work.