The points should not look like that after a month or so. If there is a big dag on the points surface then you can dress it with a nail file.
Rotate the engine until the points rubbing block is at the centre of the cam on the
distributor shaft. Check the gap at this point. I don't know the factory spec off hand. You can just eyeball it for now and make sure it opens and closes.
If you are careful you can do that test by yourself. Just be aware that the engine will continue to run until you pull the wire off.
Also pull that white wire off for now.