Skyrim glitches

Once upon leaving the Alchemy shop in Windhelm, I think I was doing the White Phial quest, I discovered that the ground had disappeared. I fell though it and landed in water below, and was able to look upwards into the town and at the bottom of buildings and things. The same thing happened once in Whiterun when I was going to visit the Yarl, little bridge and the front of Dragonsreach was just gone. The most common glitch I run into is floating weapons in the field. Say I kill some bandits and their dropped weapons get left on the ground, and I go on my merry way. If I come back to that spot on the map later, the weapons are floating still in the air above where they were dropped, sometimes falling back to the ground if I touch them. Weird shit.

Edit: Playing on a new character I made yesterday, I encountered a snow bear in the North, north of Windhelm, right on the sea on a tiny island with ice floes all around. The bear at one point ran away from me, into the water, and just disappeared. However, the little indicator on the compass bar was still there. I dove underwater just to check it out and saw the bear underwater. Running. Like it was on land. It wasn't even on the sea-floor, just in the middle of the water, underwater, running around. Way to go, bear.

 

I was fighting a Draugr Deathlord and I got annoyed with them because they're everwhere (I'm level 96) so I used Unrelenting Force, then killed it while it was on the ground. It got up, while dead, with its fists up like it was going to punch me, then just started swiveling its torso and arms around against a wall. It wasn't attacking or anything and had a search option but it wouldn't fall over and I couldn't move it and it was super creepy.