First and foremost: NEVER POINT A RIFLE AT ANYTHING YOU DON'T WANT TO SHOOT! SAFETY FIRST. USE CARE IN LOADING AND UNLOADING ANY RIFLE. That being said, here is an explanation of the problem.
All bolt action rifle safeties act in some way to cam the firing pin back off the sear when placed in the safe position. This is done so that if the trigger is pulled while the gun is on safe, the sear will "reset" or go back into place when the trigger is released. In rifles like the Mauser, U.S. Springfield, or Winchester 70, the safety is in the bolt sleeve and acts directly on the firing pin, camming it back and locking it. The trigger can be pulled, but the sear will always reset when it is released.
But in the Remington, the safety is part of the trigger assembly. It cams the sear up and back, which in turn cams the firing pin back, but it does not lock the trigger. The firing pin movement is quite small compared to that on, say, a Mauser 98. If the trigger assembly is worn, the sear may not be moved up enough to allow sear reset. If the sear is not cammed off the connector far enough and the trigger is pulled, the sear will not reset and will be held only by the safety cam itself. When the safety is released the gun will fire.
Remington has changed the manufacturing method and material used in the sear, but I do not believe the problem is fully solved. Ultimately, I think Remington will have to go to a bolt sleeve type safety. I think they could do that, and still keep their excellent trigger pull.
Obviously, the problem is greater in the older rifles, but the key factor is wear, not age. Owners of Remington 700's should perform a simple test. With the rifle empty, cock the bolt normally and set the safety. Pull the trigger and release it. Take the safety off. The gun should not fire. If it does, consult a gunsmith or send the gun to Remington before further use.
Jim