What you are experiencing is symptomatic of failure of the DLP chip. This is a very common problem with all DLP based tvs. What is happening is that DLP chip, which contains millions of tiny actuated mirrors, starts to freeze up. Those "stuck" mirrors result in a white pixel on the screen. They cannot be unstuck or repaired, the entire dlp chip has to be replaced. You will continue to get more and more dots appearing, until they cover the screen.
There are many blogs and youtube videos detailing the process, if you're inclined to do it yourself. It is about a $200 part. If you have a local tv tech out to do it, figure on around $300-400 total for the repair.
Even though it is past the warranty period, it is also worth a call to mitsubishi. Because this was such a common problem, they will often offer to cover the cost of the part, if you pay the labor costs.
If you'd like, I can help with finding the part, finding a repair shop, or even recommending replacement models if you'd prefer to go with a new tv instead. Replacement may make more sense in the long run, as DLP technology is obsolete now, other parts will continue to fail, you'll have to keep buying lamps, etc. A new LED tv of this size can be bought in the $800 range, with updated features, better picture, and a fresh warranty.
Best regards, ***** ***** for the news,
I am an independent technician and I've spent my personal time, unpaid, in an effort to assist with the question for which you solicited my services. This site works on the honor system, and to that end, I have prioritized working with you ahead of other paying customers.
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