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.