I probably wouldn't bother messing with the nut on that unless there's actually something wrong with it.
But, unlike what others have said, I don't really see anything wrong with upgrading the pickups in it. Sure, that's just a "lowly" LP Special II, so they're right when they say the immediate benefit (especially through that amp) will be minimal at best, but there are still some things to gain from doing it anyway.
1. You'll gain valuable experience working on guitar wiring without the risk of damaging a pricier instrument.
2. When you eventually outgrow that guitar & upgrade to a better one, you can take the pickups out of the old guitar and put them right in the new one. In other words, an investment in pickups is never wasted because they don't wear out & you can keep moving them from guitar to guitar.
I'll say this in defense of the LP Special II as well - sure, they're cheap. Yes, the fret ends will cut you. Yes, the body is made out of plywood (for real). It's really a Les Paul in silhouette only, as nothing else about it resembles a real LP at all. HOWEVER, than can sound good. Huge, massive, even. I have experienced this first-hand, and was shocked by it. So there's that.
