1000 grit is too coarse. Get yourself a piece of 4000 grit, and a bottle of Meguiars liquid rubbing compound. Wet sand lightly, even 4000 grit will cut rather quickly. You can then hand rub with the compound and buff to its original sheen, maybe even a little better. I would not do this until the varnish has cured for at least 30 days.  Good Luck!

   Did you need to sand?

What was on the finished coat that needed removing?

I would try making a palstic tent over the work area and build a good static charge on the plastic, and then lift a side and apply the finish and set the side down then to the other side.

I would not even use sandpaper. Get some polishing compound like 5000 or 8000 grit and polishing pads.

   Do not shake the varnish and stir slowly so not to add bubbles.

   Thanks all!! Sanded again, and revarnished. Got an acceptable finish this time, wheee!

Will take your advice Buzzy, I use 3M liquid rubbing compound on clear coat and works well so I guess it will be about the same as Meguiars. 

George, dust spots mostly. Where do I ge 5 or 8M polishing compound?

   I get mine through a Festool dealer. Originally for the automotive industry, but Festool has a series of wood sanders that can actually polish bare wood to a what looks like a finished coat, expecailly if it as oily wood.

You could also try auto parts stores or an automotive body shop.

There sanders need a vacum cleaner, dust extractor, that has variable speeds or suction power so the sander is not pulled into the working surface with enough force to create swirl marks.

   I think I would be too scared to go near boats that shiny

   After a few uses and moving form launch site to launch site that will not be an issue.

   Another approach:

Dust nibs, Final Varnish Coat and the Brown Paper Bag Trick