One would be shooting the gun at the campfire, then the camera would shoot back and the hand they shot with would be empty.
When Mark and Kurt stop to get gas, Mark pumps his own gas. In Oregon, however, you are not allowed to pump your own gas.
The trail to Bagby is much more improved than the hike they went to the springs. You don't actually traverse any logs like they do. Friends of Bagby have made bridges over any areas that would be hard to cross like that.
The birds singing at the hot springs are native to the Eastern U.S., not Oregon. According to Director Kelly Reichardt, she unknowingly mixed the audio for this scene with a stock recording of forest ambiance, and a birder pointed this error out to her at a Q&A for the film.
When they are at the café, the waitress tells them they are "within 5 miles" of Bagby Hot Springs. Truth is, there is no cafe, restaurant, gas station, or store within 30 miles of Bagby.
Early in the film, they are on Hwy 30 near the St. Johns Bridge, driving in the direction of Astoria, which is AWAY from the hot springs they are going to. Then suddenly, inexplicably, they're in Colton, and heading towards the hot springs.