D&D is a role playing game. Players play characters in the story. Tell the story, and apply the rules to the story. Don't let the rules tell your story.
My suggestions above do a pretty good job of supporting most stories, but I always ask whether the rules 'make sense' in the story as I apply them.
If the heroes are highly distracted, it should be much harder than normal to notice a trap or secret door. If they're moving slowly and being attentive, it should be more likely that they find it than if they're moving at a causal pace. If the heroes devoted resources (taking the observant feat) focused on being attentive, they should get some bang out of it by finding things people normally miss (like Sherlock). We want the rules to facilitate that, but if they accidentally contradict it - rule against the rules to tell the good story.
And then, if the DM and players disagree on something, the DM should rethink and ask if he is telling the best story - and the players should trust his or her final decision.
It really is that simple.