This will help you understand what to look for and where to look for it at as well as explain the working order of everything. https://shoot-on.com/your-101-course-in-remington-700-factory-triggers/I'm no gunsmith, so it's a little hard to know what to look for. I plan on following installation instructions to the letter when I install the new one and I'll leave it at that.
You can wiggle the trigger blade back and forth just a bit. It's like it won't reset some of the time after firing.
It could be that your trigger is gumed up and or dirty as well as lacking sear engagement. Douching the trigger assembly with brake cleaner and blowing it out with compressed air would be a good start. Increasing sear engagement is also an easy task. You may end up with a bit of creep/pretravel but that'll be better then to little sear engagement resulting in a trigger that involuntarily goes off on its own.