tonight while playing fallout nv i was in the repconn building exploring (i had rex and lilly with me) i was carrying way too much so i gave my ncr ranger armor to rex but he couldn't carry it and dropped it but before i could do anything about it i was attacked by droids which led to a tough battle which almost killed me but when i returned to where my ncr armor was dropped it was gone.

Stuff falling through the floor is bad. Mine was I was stuck in place. Like I could look around and equip/unequip my weapon. But when I used WASD to move, my character would stand in place. Forgot how I fixed it. Probably loaded a previous save. This was when the game first came out too.

Probably this one http://www.youtube.com/watch?v=nmdnHef3apE

oops i went back to the repconn hq and i found my ncr armor, not quite where i remember dropping it but oh well.

One time I was walking through the desert in the middle of nowhere, and a securitron came up to me
and told me I needed a passport to get into New Vegas. I only had one dialogue option (seriously!)
and it was the one that triggers combat. It kept killing me every time, so I had to load back, get a companion
and turn the difficulty down to prepare for it.

The people walking in air is a common glitch, with the ones stuck in a rock or in a wall.
Other common glitches I found are the feral ghouls at Repconn not appearing at all or the deathclaws jumping from the sky ( glitch already present in FO3). Some people sleeping in an already occupied bed or 2 sitting on the same chair too.
But the weirdest I've seen so far is when a freeside citizen randomy walks past the securitrons and is attacked. Then all other citizens in freeside join the fight and attack the securitrons. It happens if you wait long enough near the gate without entering the strip.

I was hunting one of the fiends when that legion guy shows up and just stares at me. No talking. Scared me half to death to turn around and he's just standing their. He would just follow me around and stand their. After about 15 min I shot him

This is probably due to mods, but I was having issues with finding an NPC, so I used player.moveto and I ended up in Zion at that house where you gather lunchboxes.
And what awaited me?
A dozen berserk securitrons from Old World Blues.
A dozen tunnelers from Lonesome Road.
A dozen police dogs from Old World Blues.
A dozen robo-scorpions from Old World Blues.
And a dozen green gecko's.

It was a cluster[censored] of hostiles.
Funny, but very very irritating.

Sounds like you had quite the party.

Body parts/heads that get stuck in the air or end up misshapen and the dancing, jigging skeletons always amused me. Or when you fast travel and you see a generic NPC falling out of the sky to land in his "spot" then casually stroll away.

I was using this smoking mod (companions smoke when idle) and occasionally their mouths would get "stuck" - akin to the way their faces sometimes get stuck in the "combat grimace". So one time I entered a cave with all my minions and when I turned around, Arcade looked http://crimsonkeep.com/wallpapers/data/media/33/falloutNV-0001432a.jpg (he was looking up at EDE).Turned out all but Cass had mouth expressions of one sort of another, so I pushed them around for a http://crimsonkeep.com/wallpapers/data/media/33/falloutNV-0001430a.jpg I must have laughed like a loon for 5 minutes. ... I am easily amused.

Radscorpions walking on their tails or on the tips of their pincers is pretty common.

One time I shot Cook Cook with something high-caliber, had a crit and probably bad Bloody Mess, so he was torn into little pieces. His bloodshot eyes remained floating in the air at my eye level on the spot where he got killed for the rest of the game (I came back a few times to check).

On my last playthrough I had a bad spawning glitch at the Deathclaw Promontory. Some of the Deathclaws did not initially spawn, and neither did the corpses with the Remnant armor. So I cleared out the Deathclaws who did spawn, then reloaded (or was it quit and re-entered?) the game to get the corpses to spawn. And the missing Deathclaws, complete with the Deathclaw Alpha Male, also spawned. I was in a bad position, basically cornered from the get go. Luckily I was playing an Explosives specialist so a couple of missiles from my trusty Annabelle (Vats + Slasher + Rocket + Jet + Sugar Bomb + Med-X) took out most of the pack and had the survivors crippled badly, so I survived. Barely.