If you want to "contemporarize" the play, you might change the clothing to better represent the contemporary upper-classes, as suggested above.
I agree also with the opinion that this play's commentary and subject matter remain relevant today and the text of the play seems perfectly understandable now.
Perhaps one exception is the inherited spine disorder of Dr. Rank. This doesn't make much sense to today's understanding of heredity, or at least his explanation of it doesn't. He believes that rich foods and "high living" on his father's part have given him a spine disease. This could be adjusted, but doesn't need to be in order for the play to be relatable.