The Crazy Eyes are an indicator of future mental instability.
In Swarley, Marshall introduces Chloe to Ted and Barney at the bar and they tell him that she has the "Crazy Eyes".
Both Ted and Barney give Marshall examples of their experiences with this malady; Barney's crazy-eyed date wanted a threesome with a teddy bear; Ted's crazy-eyed date, Jenene, picked up a long metal rod and repeatedly hit a car that nearly hit them as they were about to cross the street.
