If you are keeping it standard, points are absolutely fine and, in fact, there's a lot to commend them for. A lot of people are just lazy and can't be bothered setting them properly. As has been said, read Sticky's section on this a couple of times. Especially get your head around the fact that it is not just the points gap that matters, it's important that they open at the right place. I always used the cigarette paper method and have never had an issue.
When you start getting towards a sporty 186 kit, then maybe go Electronic, as points can bounce. Otherwise, IMO, if the stator's all good, they are fine.
You seem to have the hang of posting photos
When you get to it, I'd like to see a picture of your Slide and your exhaust manifold contact services if it is, as you say, leaking. Don't clean it or smudge it, just take a couple of pics. You'll be surprised what you can tell from this. It may, of course, be blatantly obvious when you get underneath why it is leaking but often it can be the slightest distortion of the exhaust manifold that stops it sealing.
If it was me, whilst I was there, I'd take the cylinder head and cylinder off to have a look at the state of the piston and rings. However, if you don't do this, please be meticulous in checking for any leaks from the cylinder head and base. It usually manifests itself in black oily gunge. Remember that such leaks can be deceptive. I have spent many an occasion, convinced some mating surface was leaking, only to discover it was coming from somewhere else.
Lastly, I think your plug gap is too large. Shouldn't it be .45 to .5? I'm just saying this from memory as it's a good few years since I had a standard "ish" 125 Special on the road.
Please feel free to keep asking questions. Pictures paint a thousand words too
