Don’t limit passive skill checks to just perception and insight, remember that passive skill checks can also apply to other skills (PHB pg 179). I always get a list of passive skill check values for Arcana, Dungeoneering, History, Nature, and Religion from my players. That is a long list, but having the passive skill check values for all of those skills helps in tons with running my game.
Knowing what my characters can pick up subtlety allows me to quickly dispense out information and clues. Having my players roll for each check can slow down the flow. Plus it telegraphs information and hints through metagaming.
As an example, players want to use religion to determine information about an unremarkable artifact. If they blow a roll, they know there might be some importance, but they just messed up on the attempt. If they roll exceedingly high, and I comment there is nothing noteworthy about the artifact, players know that my statement is true (and not that their skill is so low, they have no idea of its importance).
Passive checks bypass that. Also, I can cue players that something jogs their memory and they know fact X due to a passive check. Typically they will want to make an active check then and see if they can gain more information. To me that is a great way to utilize knowledge checks. If they are trained in the skill, they will pick up on something leading to them try and get more information with an active check. Even if they fail, their trained ability helped them at least gleam some info from the current situation.
Don’t forget the listed DC values for knowledge checks were changed in an errata. Common knowledge is now a DC 10 (down from 15), with paragon tier knowledge at a +5, and epic tier knowledge a +10. Being trained in a skill, with some moderate bonuses due to ability scores (don’t forget the 1/2 level bonus), you now have characters that can pick up on a lot of subtle clues through passive skill checks.
Quickly assessing monsters they encounter is also another way to use passive skill checks. Having the player roll becomes a crap shoot typically, where having them use passive checks can guarantee they have some moderate success. A high ability score, combined with trained knowledge and a few levels, means most players can pass a DC 20 check discerning a lot of knowledge about creatures in a fight.
So be sure to whip up a list of knowledge-based skills from your players. Use passive checks based on those skills more. You can speed up your game, and reward players for dipping into various skills. Anybody else doing something similar?