The title alludes to the comic strip "Hairbreadth Harry", which ran from 1906 to 1940.
The last cartoon to pit Wile E. Coyote against Bugs Bunny, following Operation: Rabbit (1952), To Hare Is Human (1956), Rabbit's Feat (1960), and Compressed Hare (1961). Unlike those entries, however, Wile E. Coyote acts like his persona in the Road Runner shorts, meaning he doesn't speak.
Bugs says that the Road Runner has sprained a giblet, but that's not possible - a bird's giblets are its internal organs.
This was the first WB cartoon to be released after Warner Bros. Cartoons closed down in 1963.
The background artistry was becoming more abstract as the decade progressed, but was no less colorful or detailed. The area depicted is once again the color country desert region of the southwestern USA.