The overall plot concerns a villain who has set up an elaborate puzzle for the FBI team, has demonstrated repeatedly that he knows tons of stuff about them, including names and addresses and vacation addresses and childhood hobbies and so on and so forth. Right. Ok. Excellent puzzle and creepiness factor all round. And when the team's brilliant hacker-girl, Garcia, realizes she did something dumb, she is suitably horrified and embarassed; that made sense.
When the villain finally tells them about their "quest," he makes it Very Very Clear that the one rule-- the ONLY RULE-- is that they can't get anybody else involved. Just the team. Immediately, Agent Gideon, who is in a foul mood, tells the relevant people to contact sketch artists and hold a press conference. Which is... I mean, you can make the argument that it's a way of drawing out the UNSUB and testing things and so on. Fine. Except... then Hotchner sends an exhausted Greenaway home to get some sleep. And, unsurprisingly, the villain is lying in wait, furious that his rules were broken, and shoots her.
Right. Ok. In the second part, Hotchner realizes that the agent he instructed to "take Greenaway home" just dropped her off, rather than checking the house, which was what Hotchner meant for him to do, since there is a crazy person out there who knows all about them, including addresses, and whose ONLY RULE has just gotten broken. Cue guilt on the part of the agent, and on the part of Hotchner. And I can't figure out if it's plot-related stupidity (how do you know, first of all, that Random Agent Guy knows the details about how much the villain knows about all of you; and second of all, you don't have a couch or bed somewhere in headquarters you could send her to, considering that you just annoyed a crazy, violent person), or if it's realistic in terms of everybody in the office being very stressed and working on no sleep and tons of caffeine and making a logical mistake.