There is an obvious edit at 2:59 after Elmer says "Yay! I twapped him!", as the music suddenly skips in the next shot and it looked like Bugs was going to reply before the next cut. It is unknown what was removed and why, so the scene is considered lost.
The second of only two Bugs Bunny cartoons directed by Frank Tashlin; the other being The Unruly Hare (1945). Frank Tashlin is uncredited because he had left the studio before the short debuted, and Warner Bros. had a rule at the time that former employees couldn't be credited. This is also why Robert Clampett isn't credited in some of his last shorts for WB. Robert McKimson inherited Tashlin's unit after his departure.
The signs Bugs holds up are all slang references to craziness: screwball, crackpot, drip, and batty in the belfry. The screwball drawing would be seen again in Duck Amuck (1953).
Bugs says Elmer is "trying to slip me a Mickey." In slang, a Mickey Finn is a drink laced with a psychoactive drug or incapacitating agent (especially chloral hydrate) given to someone without their knowledge, with the intent to incapacitate them. It was named after the manager and bartender of the Lone Star Saloon and Palm Garden Restaurant, which operated in Chicago from 1896 to 1903 in the Chicago Loop neighborhood. In December 1903, several Chicago newspapers documented that Michael "Mickey" Finn was accused of using knockout drops to rob some of his customers.
Bugs and Elmer break the fourth wall quite obviously here, and so does the bear (in a fashion). But instead of Bugs doing his signature move of kissing his adversary, Elmer plants one on the bear (which he thinks is Bugs) instead.