The Polar Bears - Seriously, stop asking about the damn polar bears. They explained them. The bear cages that Sawyer and Kate were locked in? Yeah, those were for the polar bears. Somehow they escaped when the Others drove out the Dharma Initiative. Dharma was running experiments on them.
The Hostiles - People that Jacob dragged to the Island before Dharma got there. Why were they hostile? They were protecting the Light for Jacob. And possibly killing people at the behest of the Smoke Monster. Otherwise known as the Others.
The Smoke Monster - Jacob created him when he threw his brother down into the heart of the Island. How? Who knows? It was never explained why the brother became a monster while Jack and Desmond did not. Maybe it's because he was evil at heart? Maybe Jacob willed it?
Many of the strange happenings are connected to the strange electromagnetic energy of the Island. It was never explained. That's the kind of show LOST was. It wasn't about giving the answers to every strange event, it was about the characters. Besides, just about any explanation they could give would disappoint some portion of the viewers. Life is better with a little mystery.