As Sergeant Stoddard initially interviews Hollings after the double-shooting, it's early evening at the crime scene. The scene of a shooting which occurred mid-morning at the latest, yet from which the ambulance is just now departing for the ER. Even in early fall in south-western Montana, it doesn't get dark that fast.
Only the National Park Service Rangers law enforcement division handle any crime committed within Federal Park boundaries. The state, county, or local police would not have been involved. They have no jurisdictions in Yellowstone National park. One exception is Grand Teton National Park due to a grandfather clause of that Park's late creation in the 1940s. A Wyoming State and County Highway runs through the boundary but again, criminal incidents are lead by the Park Service with assistance by County Sheriff or State Highway Patrol depending where it happened. County and State Patrols are allowed on the main highway but typically they avoid the inner park scenic road unless asked for.
When the two shooting victims are found in the parking lot, the Sergeant's head wound dressing looks exactly like it did 24 hours before. Either he's not received any additional care at home or hospital, and his blood never oxidizes to a darker colour, or his wound has begun bleeding again (unlikely) in an identical pattern.
Yellowstone's fauna, leaves, and terrain look nothing like the area where they shot this. Also the Yellowstone Park signs are laughable at best. The Park Ranger uniforms in this film are also not even close. growing up near Yellowstone Park. The producers did zero research for authenticity to match the local location, props, and wardrobe for Yellowstone National Park. They spelled the name right, that is about it.
Even given the need for locale-ambiguity in a small production like this, labeling the constabulary vehicles "Montana Police" seems a bit of a stretch. A 5-person police staff should have a municipality name attached to it.
Given the continual emphasis on the 'small town' vibe of the Diner/Car Repair/Visitor Center community, it seems unlikely a phony Park Ranger would go un-noticed among the locals long enough for multiple visits to to the diner for meal stops allow him to be thought of as a 'regular', especially with the ongoing mystery of multiple, recent, unexplained disappearances .