I imagine, that the "blips" might show leakage current of the the series pass transistor. As you find out yourself, there's no accuracy specification for Iout=0, which contradicts somehow the suggested usage as voltage reference. Of course you can't read quantitative specifications into some flyspeck on a diagram, not even the existence of these blips.
What I would do is to provide an optional load resistor in the circuit and find out empirically if it's actually required, including tests over the full temperature range.