Don’t know how many people think it’s “great,” but Diamonds (1999) starring a then-86 y.o. Kirk Douglas got me chuckling.
(I can’t figure out how I ever got the idea that its title was actually 13 Diamonds.)
Groucho Marx was no spring chicken.
And I’m ashamed of you all that I’m the first to mention him.
In absolutely no sense. I was reading through the thread and got caught up in the older actor discussion and completely forgot about the comedy part of the OP.
I’m going to claim advancing age as my excuse :p.
Well, by the time he died, at age 86, no, he wasn’t. 
While he appeared in a few movies (usually in small / uncredited roles) after the age of 65, in the core of his film career with his brothers, in the 1920s and 1930s, he was only in his 30s and 40s.
Groucho Marx turned 65 on October 2, 1955, so these are films he appeared in at age 65 or greater, and the parts are basically small:
The Candidate
Skidoo
Birds Do It
The Story of Mankind
Will Success Spoil Rock Hunter?
Showdown at Ulcer Gulch
Why is 65 the cutoff? Groucho had a pretty significant, definitely non-cameo, part in Double Dynamite in 1951, when he was 61.
Actually, I see that it was filmed three years earlier, when he was a summer chicken of 58
It’s the cut-off because it’s explicitly stated in the OP that it’s the cut-off.