PDB Mining: Why Do I Find Atoms Less than 1 Angstrom Apart?
if you are using NMR structures you might be making the mistake of using several superimposed structures - it would be nice to develop with x-ray structures at less than 2.0 A resolution for starters. 

Some of the models at low resolution can be sloppy, but submitted after 1994 or so will not have any center to center distances as that's when the x-ray structures used molecular models rather than just electron density rigorously and wierd steric violations in the structure should be rare. 

Still, this might not be wrong - the hydrogen might be pointing right into the aromatic ring's center.  This has been observed quite a bit.  In such a case, the atom to ring plane distance might be very small.  

You only need to worry if the center to center distance between atoms is less than the vanderWaals radius.   I would filter for atom center to center distance and see if you see violations.