The completeness of quantum mechanics (thesis 1) has been attacked by the Einstein-Podolsky-Rosen? thought experiment which was intended to show that there have to be hidden variables in order to avoid non-local, instantaneous "effects at a distance". [Bell's inequality]? about the measurement outcomes of such an experiment was derived on the assumption that these hidden variables exist and no non-local effects are present. In 1982, Aspect finally carried out the experiment and found Bell's inequality to be violated, thus rejecting interpretations that postulate hidden variables and local interaction. This experiment has since been criticized and improved experiments have been described by Weihs and Rowe, confirming Aspect's results.
Of the three theses above, the third is maybe the most problematic from a physist's standpoint because it gives a special status to observation processes without cleanly defining them nor explaining their peculiar effects.
Many notable physicists and philosophers have objected to the Copenhagen interpretation, both on the grounds that it is non-deterministic and that it relies on a non-physical observation process to create reality. Einstein's quotes "God does not play dice" and "Do you really think the moon isn't there if you aren't looking at it?" exemplify this. Schrödinger's cat was originally intended as an example to show how absurd the model was
The main alternative to the Copenhagen interpretation is the Everett many-worlds interpretation.