An e0 outfielder should not have any fielding or throwing errors.
An e0 catcher should not have any fielding errors but could have throwing errors.
A T-0 catcher should not have any throwing errors but could have fielding errors.
An infielder should not have any errors outside of an x-roll.
FYI, this was my error-free theme team. 32 errors. Won a ring. Goal was to maximize power while minimizing errors. Range was not a primary concern, so I had a lot of guys with a defensive rating of like 3e1.
http://365.strat-o-matic.com/team/1388695