Just guessing here, but I suspect you partially dissolved the finish when you used the minwax "wood finish", which is actually a stain, and mostly meant to be used on raw wood. I don't really know what finish was on your table - shellac might be a possibility given the whitish haze that developed - that's pretty common with shellac from moisture exposure, but might also be lacquer. I suspect you're going to have to strip the table to fix it, but you might try wiping with denatured alcohol - it the finish is shellac, that will dissolve it fairly easily. You can then stain if desired using your Minwax product, then finish with shellac or something else if you prefer. Should be minimal manual labor. If the alcohol doesn't do anything, you might try lacquer thinner, but I wouldn't be too hopeful that would help much. Also might consider asking on woodcentral.com - there are some pretty good finishing experts over there.

HTH,
John

This product is actually not a wood finish, but a stain and meant to be applied to bare wood. I think you got bum advice from the hardware store.

Pine is notoriously soft and dents and impresses easily. It's hard to say what you saw originally. Almost 98% certainty it's a lacquer product that's on there now, if it was the factory finish.

I don't know if you have a salvageable situation now or not, without seeing it and perhaps without trying some things. You might try a little mineral spirits as a lubricant and buff gently with 0000 steel wool. But I suspect this will not do any good, as the nasty stuff is in the low spots.

Even if you do strip it (with a chemical stripper, please, not by sanding), pine is also notoriously difficult to stain evenly, particularly with that series of Minwax products, even when preceded by the Minwax Stain Conditioner, when used as directed. A high quality gel stain would work much better.

Sorry I don't have better news and an easier answer.