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.
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).