Bugs Bunny' final line, "I sure hope Petrillo doesn't hear about this!", refers to James C. Petrillo, the then-current president of the American Federation of Musicians, and his disapproval of recorded music, as this short was being created.
When Bugs says, "they say music calms the savage beast" he is misquoting a line from the play "The Mourning Bride", Act i. Sc. 1, by William Congreve (1697). The correct quote is; "music hath charms to soothe the savage breast, to soften rocks, or bend a knotted oak."
Bugs Bunny's remark, (to the larger & muscular gorilla); "I've seen you before. I never forget a face - but in your case, I'll make an exception." is a line from the inimitable Groucho Marx.
When Bugs muses that the ape must be a "Bar Bell Boy," he's referring to the new fad of physical fitness becoming popular. Jack LaLanne would launch his TV fitness show the following year, and California's Muscle Beach was already a local fixture.
The classified ads surrounding the hurdy-gurdy ad are reflective of the time (1950) this was made. Business real estate prices, apparently in Jacksonville, would seem remarkably low now and at least two of the want ads (to the left of Bugs's finger) are requesting white workers only.
Update: The two want ad requests for "white workers only" have been digitally removed in recent airings on "Toon in with Me."
Update: The two want ad requests for "white workers only" have been digitally removed in recent airings on "Toon in with Me."