You should register the callback in the zone, using

  var currentZone = Zone.current;
  _onErrorZone = currentZone;
  _onError = (callback == null) ?  null : 
       currentZone.registerBinaryCallback(callback);
Notice that that makes the stored function not necessarily be the same as the argument to the setter.
It might be a case where there shouldn't be a getter.

(Why is there a getter? What is the expected use?)
If you don't like having a setter without a getter, you can use the format used by StreamSubscription with .onData(callback) instead of .onData = callback.

Consider not storing a zone if here is no callback. But better yet, use bindBinaryCallback instead to store the zone inside the callback instead of on the side:

  _onError = callback == null ? null : 
        Zone.current.bindBinaryCallback(callback);