Remington "Walker" type triggers had issues with the sear not engaging properly if they were dirty or not adjusted properly.
It was a known issue for decades, and could have been fixed cheaply, but "greed" got in the way.
Remington finally went to their X series triggers, which are drop in replacements for the older Walker types.
The thing is, they are a "heavy" trigger IMHO, and the only way to make them acceptable is to replace them with something better.
The issues with triggers weren't just at Remington, as other trigger types will suffer similar maladies if they aren't kept clean or their adjustments allow them not to have positive sear engagement.
Walker sears were "rounded" on the edge contacting the sear, when this wore or engagement was adjusted beyond the flat spot of the face, the sears would "slide" off the rounded section and allow the firing pin to travel to the primer.
One of the first things I used to do with all of my Remington rifles was to stone the leading edge of the sear to a razor sharp edge. The second next thing was to insert the assembled bolt back into the receiver, set the bolt and drop it four feet on its buttpad onto a concrete floor, at least 10 times to make sure it wouldn't release at the setting I was happy with. I also honed the contact surface on the cocking piece to a razor edge.