The Pecos river originates in New Mexico, then flows south to join the Rio Grande in Texas.
Bugs, in caricature, appears in the opening credits card, engaging in several cowboy like activities.
Canasta Flats is named for the popular card game, Canasta.
Bugs mentions he'll carrom a shot. This is a reference to a popular board game that originated in India. The object was to ricochet playing pieces off the board's corners, much as Bugs does with his bullet.
Just before going out to face Yosemite Sam, Injun Joe hands off his beer to another cowboy in the saloon, saying "Here, holdum beer". Sixty-five years later, the saying "Here, hold my beer" is still a prelude for the speaker doing something dumb.