What separates a "good" eye diagram from a "bad" one?
The eye you show is firmly in the category of "good" eyes. There's nothing there that should cause an error any more often than once every 100,000 years or so.

Some things to look for: 


Are you sending real data while measuring the eye? An idle pattern or similar behavior could create an eye that looks much cleaner than the eye would be with real data.
Is there any external interference that could be causing intermittent degredation in the eye (that wasn't captured in this case)?


For comparison, here's some "bad" eyes, taken from Google image search.

This is a case of substantial random noise:



The lower eye here shows a strong duty cycle distortion:



This eye shows a substantial intersymbol interference (ISI). This eye would probably still achieve 10-9 or better bit error rate (but then it looks like it comes from a noise-free simulation):



The eye on the right here shows ISI with a shape that's characteristic of \$\sqrt{f}\$ attenuation (which typically comes from skin effect loss).



The red eye shows the effect of a reflection in the transmission line:



These eyes show strong jitter effects, maybe caused by a clock-data recovery circuit being made to work beyond its capabilities: