Well your tuning problem is strange. I am pretty sure it's not the nut as that would affect all the notes, not just a single one at the second fret. Did you try changing the string? (though even that doesn't seem like it could be the problem).
If you tune so that 3rd string, second fret is tuned to A, are all the other notes on the string then out of tune?
When you adjusted the co-ord rods, did you check that you didn't put the rim out of round? I know that in the Steve Huber video, he suggests adjusting the action like this but most of what I have heard is that this is not really the recommended method for if you crank the rods too much, you can start to egg the rim.
You can also adjust the action by getting a taller or shorter bridge, shimming the neck where it meets the pot and with the truss rod.
Of these, the truss rod adjust, like co-ord rod adjusts, are not recommended but I do the the truss rod adjust whenever I want to fine tune my action. Though like the co-ord adjust, we're talking very small moves here, about a one-eighth turn max either way.
Check that all the nuts are tight, including the one holding the tailpiece. Also, if your tailpiece has moving parts (like a cover) I would check to see that everything is tight there too. And like I said, check the tuners. Make sure the posts are tight and the knobs are tight as well.