Two true ones (my wife was a tour guide in the BH):
1: What do you do with Mt Rushmore in the winter time? “We put it in Rushmore Cave.”
2: A lady from the east coast accosted my wife demanding to see a dangeroo on the Custer State Park wildlife loop. My (then teenaged) wife looked at her and politely said “What the hell are you talking about?” Old lady from the east coast, “The sign said Buffalo and Dangeroo, I want to see a Dangeroo, dammit.” My wife responded “You read the sign wrong lady. It said Buffalo are Dangerous.”
According to someone I know who had a cousin who worked at Yellowstone some common questions were such as "when do they let the animals out" and "when do they turn on the geysers"?