Although she liked the idea of working with Robert Mitchum, Monroe wasn't impressed with the story and didn't see it as good use of her high visibility and talents. She thought it a pretty ordinary Western. Preminger, for his part, was assigned the movie because of his contract with 20th Century Fox and disliked that arrangement so much he bought out the remainder of the contact after he finished River. Monroe's disdain, her acting coach's clashes with the director and Mitchum's drinking didn't help workplace harmony much.
Preminger does take full advantage of the then-new CinemaScope technology to showcase the magnificent northwest Canadian scenery that stands in for the Northwest Territories of the U.S. in 1875. Matt Calder (Mitchum) is homesteading there and has sent for his son Mark (Tommy Rettig), who had been staying with relatives after his mother died. Mitchum had not seen the boy since he was very young (the reason is an important plot point). He meets him at a mining camp where Mark's guardian had been supposed to deliver him, and where Mark has been taken in temporarily by saloon singer Kay Weston (Monroe). Matt and Mark depart for their farm, but a couple of days later they meet Kay again, as she and her fiancé Harry are trying to float down the river to the claims office and file a gold mine claim Harry won in a poker game. Matt tells them they won't make it so Harry steals his rifle and horse for the quicker overland journey, injuring Matt in the process. Kay stays to tend him, believing Harry will return soon. But the homestead is attacked by Indians, and Kay, Matt and Mark must flee down the dangerous river on the raft.
Preminger's success had come in character-driven noir movies, so some of his action sequences didn't match their counterparts in other mid-50s Westerns. He tended instead to focus on the story between the two leads and between them and Rettig, who played 10-year-old Mark. Despite Monroe and Preminger's later derision for their work here, it's actually pretty good. It's a simple story but it works, probably because Mitchum was a great actor, Monroe was a better actress than her image every really let her be and Rettig a great foil for them both. De-glammed and spending most of the movie in jeans, some of the focus could move off Monroe's sex symbol image and onto her performance. Mitchum's tough-guy with a past as well as a code of behavior is familiar territory for him but one he does better than most before or since. Preminger's stagy fight scenes also help turn our attention to the characters instead of the expected Western set pieces. Much of the raft action looks impossibly fake to a CGI-trained audience, so perhaps we're not as distracted by its relatively low-key appearance as a 1954 audience was.
It's possible that some of the love shown River these days has to do with watching icons Monroe and Mitchum and less to do with the movie they made, but both were icons at the time and still turned in solid performances instead of just showing up. Whatever the reason, River of No Return enjoys a better reputation now than it did in its day, and that's not a bad thing at all.
(PS -- Monroe sang her own songs in the movie, and Mitchum sang the opening title track. Both did quite well. What might have been, had they lived in an age of YouTube.)