There are a couple of gunsmiths who advertise online who you can send the trigger group to and get it back better that it came from the factory. The best I know of is on Survivor's SKS board and goes by the screen name 'kivari'. The triggers can be OK to terrible, and even dangerous from the factory. A trigger tune can save you a lot of trouble and generally make the often maligned SKS a much more pleasant shooting rifle.
The way to test an SKS trigger to know if it's just crappy or downright dangerous involves two things. First, clear the weapon. Next, cock it and engage the safety. Bang the butt of the gun on the floor a few times. Go ahead and hit it as hard as you are willing to hit your floor. Do it on a carpet and you won't hurt your floor. Don't worry, you won't hurt the gun. Now, check and see if the trigger mechanism slipped and let the hammer down. Pull the trigger firmly with the safety on. The safety on these guns works, if it is right. If not you are only a small parts replacement away from a safety that works. You really want that.
Next test is for the sear engagement. Again. do this with a cleared weapon. Cock the action. Now, remove the dust cover, recoil spring and bolt/ bolt carrier group. Now look closely at the hammer as you slowly pull the trigger. It should pull back a little before breaking free and flying forward. That means 'positive sear engagement'. If it creeps forward before breaking, that means 'negative sear engagement', and that's dangerous. If you have positive sear engagement and your safety works, the trigger group is safe. Now you just have to decide if you are OK with the crappy third world trigger feel. If it's not safe, you definitely need to send the trigger out and get it fixed. They usually fix the engagement points and put a new US made spring kit in, which helps the overall feel of the trigger.
Because of the 'positive engagement' design they will never have the super light trigger pull that you can get on some bolt actions. With a little work (or a little money having that work done) they can be way better that most SKS are. It's a good design that suffers from typical Communist execution. Lacking in attention to detail on the line. These weren't built by the same level of skilled labor that Colt had in the 1960s. It's nice that you can just send in the trigger group of the SKS. Saves shipping cost and doesn't involve transfering the FFL part.
You can pick up an aftermarket firing pin with a return spring for really low money ( I think I bought one for $15 last time I needed one). That will prevent any slam fires. Not usually a problem with Russian ammo, but it happens sometimes if you use American ammo in an SKS. The primers on USA ammo are thinner than the Russian ones.