The jury is still out on whether Einstein's equations on general relativity were right, though. That's why they sent up a sattelite last year to test them.
Special relativity is the one that has been proven beyond any reasonable doubt.
I'm not exactly sure what you mean by that. There have been confirmation experiments since 1919 that have validated general relativity. The modern confirmation experiments tend to be more on the order of determining if general relativity is still accurate to some insane number of decimal places (similar to the experiments with QED). Physicists generally hope that there is a bump or an error in their measurements because it means that the theory is not completely refined, therefore giving them something to do! It may come to be that there is a certain range of velocities or masses at which GR does not follow observations (and physicists certainly hope this is the case!), but then it will be put in a similar place as Newtonian mechanics--valid over only a certain range.