The only way I know of to eliminate "runs" in paint or varnished finish is to wait for the coating to cure completely, sand out the high spots, and re-coat. If you try to sand too soon, the coating will gum up the sandpaper, and it will not be possible to obtain a smooth surface.

That drying time is going to be several weeks. I have been able to carefully use a single edge razor scraper ti scrape off the run---shortening the drying time to a couple of days so sanding is possible.

Patching poly is almost impossible, it does not feather into an existing coat. So, you have to recoat the entire surface that had a problem.

You may wish to try either wiping urethane or gel polyurethan to avoid drips on vertical surfaces.

http://www.woodkote.com/products/Polyurethanes/JPK.pdf

http://www.taunton.com/finewoodworking/pages/w00075.asp

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