In the train car on the way to the dude ranch, Willoughby (Lou Costello) sees Duke (Bud Abbott) and several cowboys getting ready to play cards. He says, "What are you playing?" and Duke replies, "Poker". Willoughby says, "I've never played that game before. Is it like dice?" That's an inside joke, referring to Abbott & Costello's famous dice routine, which they used in their first starring film, Buck Privates (1941).
When the dude ranch bus pulls into the station to pick up the train passengers from the wild west show, the signpost on the depot reads "Gower Gulch". That is an inside joke, as "Gower Gulch" was a longtime name for the area of Hollywood--centered on Gower Street--where many low-budget independent producers and studios, which specialized in shooting westerns because they were cheap to make, were headquartered.
This was the last Bud Abbott and Lou Costello film to be directed by Arthur Lubin. Like their previous collaborations, this became one of the biggest hits of the year.
During the car chase scene, Bud Abbott says that he can't drive. This references Abbott's real-life inability to drive due to being epileptic. He never drove a car in his life.