As a crusty curmudgeon, I imagine that John Simon was in the same camp as Al Capp in regards to Lennon/Ono during their bed-in. Al Capp was notoriously nasty - this clip demonstrates:
One of the ways that Al Capp reminds me of Simon is the way he disparages Yoko's appearance here in an amazingly nasty and blunt way. Simon is infamous for making snide remarks about actors' appearances. Roger Ebert had one of the best come-backs:
"I feel repugnance for the critic John Simon, who made it a specialty to attack the way actors look. They can't help how they look, any more than John Simon can help looking like a rat."Simon is officially working for the Yonkers Tribune although he doesn't seem to have written anything since last year.
I still haven't found it in their online archives, so I have no proof, but I distinctly remember about ten years ago on Theater Talk, John Simon suggested that Suzan-Lori Parks was a "social climber" because she married a white guy. I still can't believe he said that.
Fun fact: John Simon once dated Katha Pollitt.