On the Accuracy of Galileo's Observations
  Galileo Galilei had sufficient skill as an observer and instrument builder to be able to measure the positions and apparent sizes of objects seen through his telescopes to an accuracy of 2" or better. However, Galileo had no knowledge of wave optics, so when he was measuring stellar apparent sizes he was producing very accurate measurements of diffraction artifacts and not physical bodies. 
Christopher M. Graney