Are there any measurable world records from the Elizabethan era that still stand?

I'm not sure what sort of world record you would have in mind, and given the parlous state of science at the time, what world records would you trust? If, for example, I exhibited a Chinaman from the Ming who lived for 231 years, which is surely a world record, you would rightly reject this by saying 'it is much more likely that this world record is inaccurate than he really did live to 231, given how notoriously bad records were at the time, the cultural value set on being the oldest man in the world, etc'.

If Shakespeare got pretty close to the perfect tragedy, but there was a slight refinement of the form from the 19th century that's better (if less significant), surely people would prefer to watch that, and count themselves fans of that author.

If Shakespeare helped define what the perfect tragedy was, and all later tragedies felt the 'anxiety of influence', this isn't so clearcut. See my other comment.