I had a random thought the other day after reading a discussion about the lack of passive perception in the D&D Next playtest. The way I see it, the advantage of passive Perception is that it speeds up task resolution, but more importantly it allows the DM to gauge the party's awareness by not alerting them to the fact that something's up (which is obvious when the DM asks you to "make a Perception check").
The disadvantage, of course, is that "assuming the average" can get pretty boring since you know you'll always succeed at a given DC. Does this realistically represent awareness? You can assume that the adventurers are always "on alert" and cautious, but nobody can spend 100% of their day completely focused on every little aspect of their environment. Trust me, I do bird surveys for a living and it's tough to keep track of every individual singing and calling around you even for just 10 minutes. To suggest that an adventurer is constantly equally aware (unless they're "actively searching," in which case they can do worse) is, quite simply, pretty absurd. Minds wander, people daydream, sometimes people are talking with each other and other times they're silent, and perhaps most importantly sometimes people focus on the wrong thing. You can't give everything equal attention, so why assume that you're always focusing equally on The Thing That Matters regardless of what it might be?
My solution - the random number table! No, really! A DM can simply roll up a list of random numbers between 1 and 20 (easy enough to do in Excel), crossing off each number as it gets "used." You'd also need a reference sheet with all of your player's modifiers (which is no different than keeping note of their passive perception scores, really). I'm constantly scribbling things down when I DM, so the players would be none the wiser that I just "used up" a perception roll for them. If you work from a laptop you could even use an electronic dice roller without your players knowing.
I haven't tested this idea in play yet, but theoretically it combines the advantages of passive perception (fluid play and not cluing your players in that something's up) with the advantages of rolling (simulating random chance in a variable task). Win, win, if you ask me.