Posting this just in case it helps someone else.
Purchased a house that came with a wall-mounted Samsung 65" Model UN65F6300, which had been working perfectly since we moved in. Recently purchased a Samsung 43" (UHD TU-8000) for our outdoor gazebo. The TU-8000 comes with one of the new slim-line remotes. Did not want to keep the remote out in the weather so I placed it on the mantle which happens to be just below our 65" TV.
Problem I started having was that the mute icon on the 65" would start flashing, the power light on the 65" would start flashing, and the remote would not work correctly (i.e., I would, for example, press Menu on the remote...menu would display for a second or two on the 65" but would then go away and the Mute icon would flash). So, could not access Netflix or Prime via the remote, and the volume was constantly cycling on/off on the TV.
Went through all of the troubleshooting tips I could find online (unplugging 65" and letting it sit for a few minutes before powering back on, resetting the TV, pressing combinations of buttons on the remote to re-pair with the TV) and nothing worked.
Was getting ready to pull the 65" TV off of the wall mount to check for a blown capacitor or damaged power supply....so I cleared everything off of the mantle below it (including the remote for the TU-8000) and all of a sudden the problem stopped. I put everything back on the mantle and the problem started up again. Figured the remote was the most likely candidate so moved it off the mantle and problem stopped. Have since moved the remote for the TU-8000 several feet away from the existing 65" TV and for the last couple of days have had no issues.
So apparently even if the slim-line remote is not even being used...if it is within a couple of feet of the UN65F6300 there is some kind of feeback or IR issue that causes some very strange behavior.