Another bug (original post updated):

Dead bodies show items - Earlier, after killing Ezreal, I could see his items update in the scoreboard as he bought them while he was dead. My guess is because his body was in sight and that allowed it to update the item display in the scoreboard.

I hope somebody from Riot is keeping an eye on this thread, I really am trying to help. Also would still appreciate input on whether to make a new topic with the correct name (because of that forum bug that won't let me change it).

More bugs...

• Projectiles don't show out of bushes - When (for example) Nidalee throws a spear out of a bush, the spear does not become visible immediately after leaving the bush, but a bit after. This means that someone can get hit by a spear without ever seeing it coming, when they really should see it.
• Zyra's passive triggers on Guardian Angel death - (Reported by willdem) Apparently, Zyra can fire her last missile while she's temporarily dead with Guardian Angel reviving her. This one was reported by a friend, though I have not experienced it personally (I don't really play Zyra at time of this writing).

i have the mouse in the box bug about 8/10 times plz riot fix it

Singed throws sideways - Singed often throws enemies sideways, instead of behind him. I remember it happened a few different times during a game a while back (though not always), so it's probably pretty easy to reproduce.

Jungle monsters targeting bug - After the big season 3 patch, which included changes to the jungle monsters, champions can attack monsters and get them to attack the other team. This has gotten me killed before - was running away past some creeps, a skill shot missed me and hit the creeps, and the creeps finished me off. This is very easy to reproduce; just stand next to some creeps, get a ranged enemy character to attack or use an ability and watch them attack you. My proposed fix would be to have the monsters only attack heroes on the team that originally attacked them.

Corki's missiles explode early - Occasionally, I've seen Corki's ultimate missiles explode early, before hitting anything.

Singed throws sideways - Singed often throws enemies sideways, instead of behind him. I remember it happened a few different times during a game a while back (though not always), so it's probably pretty easy to reproduce. As I recall, this generally happened while both heroes were moving, and I think perhaps the one who was thrown moved to the side sometimes? Just try the typical scenarios with Singed and I'm sure it will show up

Not a bug, poorly positioned Singed. Champions with larger models or the closer singed is to the target the harder it is to tell where he is in relation to the target.

No Damage from spells. this happens in all maps. I just played an ARAM and was executed I want to say 8 times while being slowed from Talon (somehow denied me from feeding talon a penta kill.. we were trying to throw), hit multiple times by Sivir, and any number of things. I took damage but I was still executed.
No Damage from spells. I second the gragas ult and jarvan ult.

Jungle targets, this is annoying feature that they said they hadded... "jungle camps will target whoever is closest". This has to be the dumbest thing ever for a few reasons. Say I'm chasing someone, they run past golems and I don't have vision on them I can hit the golems from far away and see which path the enemy took... If they went into the bush or which corner they went around. They can also as the OP said, kill you for the chasing team.

Aegis Cooldown? - To my knowledge, I don't think Aegis of the Legion should have a cooldown on the buff... it was also stuck that way, not changing (see attachment).
This is a graphical glitch that was on oracles in S1, S2, it's on the dominion and proving grounds map with the passive buff.