I took a damp (water) microfiber cloth to my 16' MBP screen and it looks a million times worse than it did before. There's smearing all over that won't go away even with a dry microfiber cloth going over it. In short, it looks like hell.
Is there anything I can do to fix this?
There's nothing wrong with your MacBook (needing to go in for a repair/replacement, anyways), and I know exactly how to fix this.
First, you're need a SuperCloth (search Amazon, they're gray, about $10 each - no affiliation). Next, cut one in half, they're pretty big. Take one of the halves, and get it very wet using tap water. Then, wring it out throughly. Next, wipe your screen with this damp cloth, using just moderate pressure. Finally, use the dry SuperCloth to come behind and wipe up the slight bit of moisture left behind from the wet cloth.
This is 100% guaranteed to work, I use this method every day with various screens. I've tried every type of cleaning method under the sun, this way works every time.