Black spots like little bugs on screen and some white spots

an aphid friend is an ant as they milk the aphid to use in the nest
The natural enemy of the aphid is the lady bug ( little domed shaped bug that is red with black spots )
so remove the ants and let natural predators do the job
the aphid controlle is -white oil and there are organic mixtures that you can use that you can make at home
search -- organic remedies for the control of aphids

They are called midges.

Spot remover. Black marker? Maybe not. (;^D).
Really, if it's just a little white dot on the screen, it may just be a bad pixel. Those things happen. The manufacturers warranty against more than 'so many' bad pixels, but if there's just one, I doubt they would replace it. If it's a big block of white, you might be able to get it replaced.

could be bed bugs

Sounds like you have some bugs that are boring in and laying eggs and larve are hatching. Is the first two feet of the trunk painted white? Try Googling your question, there are several sites that address this problem. https://extension.unh.edu/resources/files/Resource001830_Rep2590.pdf

I have two of those spots one bright, and the other one a little less bright.

If it's possible I'm going to send it back for a replacement.

I have the "[Bug 6334] random HW watchdog reboots" on my device as well that is quite annoying.

Was this set moved or transported? Is it possible someone struck the screen even if mildly?

If you can take a few good pictures and post them somewhere on the internet and provide the location--seeing what it looks like might tell what is wrong.

A classic description: set comes on but is a black swirling cloud where images can be dimly seen but are not clear--gets a little better after a few minutes but never gets normal.

If you wish to get some details; visit the site linked here. Pull up older posts.
http://electronicshelponline.blogspot.com/
faults & possible causes to LCD & Plasma screen are given with illustrations. You can get an idea about the fault to an extent. Faults to all LCD & Plasma screen are similar, irrespective of its brand and screen size.

It is the chip that controls the millions of mirrors inside the tv. If they are black, they are stuck closed. If they are white, they are stuck open. I JUST had the same the same thing happen with mine. I bought it 3yr and 2 months ago and I had an extended warranty on it for 3 years. Well, needless to say, it was out of warranty and I was pissed. The store I bought it from suggested I call Samsung. Which, I did. They asked for the model number and told me that my model (hlt5675sx) was one of the ones that is covered becasue they had a problem with the chip. Within 2 weeks, my tv was fixed by a repairman who came to my house. It works perfectly, now and it didn't cost me a penny. Good luck.

Can you elaborate a little? On the screen? Is it an image issue? Is there something on the outer glass? Or something between the two panels?