On that trigger, the safety is primarily a flat piece of steel with a lever bent to a specific shape meant to protrude through the slot in the stock. The mechanism pivots on a pin running through the trigger body. There is a detent mechanism on it that provides positive positioning in the safe and fire modes. There is also a small bend on the front of it which rides in a slot in the bolt release. If you push the safety all of the way forward, it pushes the bolt release down and allows the bolt to slide out of the back of the receiver.
The safety works by not allowing the main sear lever to move when the safe mode is engaged. There is a small protrusion on the side of the sear that sticks out beyond the side of the trigger plate. When the safety is engaged, the flat steel safety plate comes up under this protrusion and prevents the primary sear lever from falling. When the safety is disengaged, there is a cutout in the flat safety plate that allows the primary sear to fall.
The trigger is meant to be used normally with a pull above 24 ounces (my estimate) or more. Then, when a light pull is required, the set function can be used to obtain a pull of just a few ounces.
What happens I believe, is that sometimes people try to set the main trigger pull down to a point that is too low to be properly held by the normal trigger function. When the safety is engaged, the trigger may be pulled and the internal sear surface releases and does not reset. The gun doesn't fire though because the primary sear is held in place by the safety plate. However, the act of moving the safety from safe to fire mode at this time will release the primary sear and the gun will fire.
Is this the behavior you are seeing?
If so, you may be able to correct the problem by increasing the basic trigger pull via the adjustment screw just ahead of the trigger lever on the bottom of the trigger. Turn it clockwise / in to increase the normal pull. It is unlikely that you will need to adjust the other screws for engagement or overtravel unless the previous owner messed with them himself and thus put the trigger into a precarious operating range.
Of course, you could be having another problem altogether. Perhaps caused by a broken spring, etc.
If I have time this evening, I'll post some pictures of all that blather I posted above so that you can see what I'm talking about. If you decide to get something different, please keep me in mind if you sell it. I would encourage you to try and make it work though as these are usually very good triggers.
In the picture below, the safety is not in one of the detents and is actually 1/2 way between fire and safe. If the safety thumb lever is pushed forward a bit farther, you can see how that silver protrusion on the sear would be in the fire mode because it could drop all the way into that notch.