Going along with what TK said earlier, and mixing a little bit of Tobian's ideas, what if someone finds a cute, people friendly creature and finds they make good pets. They seem to adapt well to their new life as companion animals, and their owners say they and their new friends seem so content together, like they can feel the contented nature of the creatures improving their moods.
Untill about a year later, when the 'mating season' starts! Turns out, they ARE telepathic/empathic. That feeling of happiness you get while petting one is infact the creature's own feelings. however, like many cute species here on Earth, mating season is a time of territorial defense, mate seeking and challenging rivals. You could have your players actually do this, or the equivelant; ("No one better use MY PADD!" ; "Have you seen Lt. Jeris?" and my favorite "I think you're a terrible captain! I don't think you could even beat me, a lowly Ensign!")
As the situation decends into madness, your crew is gonna have to figure out some way to screen out those thoughts. You could use phermones if you want, instead of telepathic signals.
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"Yes, it's the Apocalypse alright. I always thought I'd have a hand in it"
Professor Farnsworth