Years ago, someone posted that Roth's coughs in the "business we've chosen" scene are evidence of congestive heart failure. But, I think he overemphasized his ailments to make himself look weak...
However, in that particular scene Roth was so angered by Michael's question that it's doubtful he would be overemphasizing his ailments at that point. In fact, it apparently took all the strength he had to get up and respond in the way he did.
I do always marvel at that cough, which was likely a masterful addition by Lee Strasberg to convey how ill the character really was.
