The field full of 1A signs, the narrators comment "Oops, forgot about the war. ", and the pitcher with the number 4F are all references to the number of men in military service at the time. 1A was a prime draft classification while 4F was unfit for service.
The action takes place at "W.C. Field," which obviously takes its name from W.C. Fields. The line "The guy who thought of this corny gag isn't with us any more" under it clearly alludes to the fact that writer Rich Hogan had already left MGM (though he returned in 1948) when work on the cartoon was in progress.
This is the only cartoon from MGM that doesn't open with the MGM lion. It is also the only MGM cartoon that gives the credits at two separate times - the title, which credits director Tex Avery like most of MGM's shorts do, at the beginning, and the rest after about 35 seconds.
The outfield sign advertising Toothodent with delirium is a play on Pepsodent with Irium.