This is the part i hate about writing, people and all their rules. 'Don't do that' 'This isn't allowed' 'I before E except after the 5th step of the hero's journey' "You know, I've never liked being told what to do." I was certain the cat had just spoken, however, I was even more certain telling anyone would land me in the madhouse. Little did Ginger's former owner know, this was no isolated incident. Animals all over the world were becoming sentient. The song was coming to a close; these were the the days of cats and dogs, no more reigning men. Hallelujah.
Yep. And the same is true of 3rd person limited (or close or whatever you want to call it). The narration can only reflect what the POV character sees/hears/knows. To give other information you have to slip into omni there, too. I don't think I've ever written anything with omni... maybe should give it a try.
I think the point people were making is that it's absolutely "unfortunate" to start being omniscient in first person, but it's not at all unfortunate to "sway" from omniscient to limited in third. It's done quite often, with very good effect. It would be a problem if it were done accidentally, or without proper care, but it's a useful tool for an author who can handle it. So some of the things you mention in your post are problems, others are useful tools, and you seem to be lumping them in together. Does that make sense?
