edit: when people correct things in this list, will just asterisk (*) them and summarize what they say. Things in the list that are questioned I'll leave untouched until someone says its been tested and shown to be wrong. If the OP wants, he can incorporate this list into the OP or into a google doc, if not after a few days I'll add other bugs to this list and make a google doc.
A lot of this is going by memory, some of it hearsay, so please correct me if any of this is wrong.
Confirmed:
1. Heal on Kill and Heal on Hit stats are able to pick you up from being knocked down if triggered soon after being knocked down. Can have pretty broken synergy with some abilities and a weapon.
*2. Bleed on hit and when being hit stats do nothing. (BeardyMcGoo says bleed on hit applies sundered)
3. Barrier ring doesn't work
4. Static Cage ring approximately doubles duration.
5. Cloak of Shadows, Rally, and Thousand Cuts rings don't apply to any abilities in multiplayer.
6. AoE daggers do not count towards dagger kills or dagger challenge points, and only one needs to be slotted (in the main hand) to gain AoE animation for both hands.
7. Focus stat not applicable in multiplayer.
8. Berserk makes you take 100%/200% more damage and only gives you 10%/20% more damage. If that isn't broken I don't know what is.
9. The Pull of the Abyss effect of Sulevin is about two second duration. This may be intentional but it is different from normal PotA.
10. Crafting one of the original tier 2 reaver armor (I believe dread reaver dragonbreath) will preclude you from crafting dragonblood. They might have ninjafixed this, but if they did, it wasn't implemented a month ago and I had to get my dragonblood from a commendation chest.
11. Assassin can get a level 54 armor from chests, looks like tier 1 armor with 0 armor rating.
12. Upgrading equipment with crafting materials that give stats with decimal numbers can result in rounded up and rounded down final stats. I don't know if fractions are still there or the rounding up and down to whole numbers as displayed is what is used.
Suspected:
1. Walking Bomb ring seems to increase damage about 40-50%. Limited testing after wondering why my almost afk necro got some kills.
2. Heard from friend Chain Lightning ring does more damage than it should.
3. Heard on forum some weapons' explode on kill stat (if I recall right) will do damage that is a % of the damage dealt by the killing blow.
4. Heard on forum Staff of the Dynamo 20% more damage if damage not taken within last 5 seconds is not working.
5. Heard on forum Pyre of the Forgotten says it has two upgrade slots but they don't work. (Xhal below says it is working. Did you confirm the HoK with HoK ring removed and without death siphon?)
6. Heard from lots of people that a large percentage of the rings are just messed up, but can't recall which ones. Bioware should really just test and fix all of them.
7. I think I have seen confusion grenade make affected enemies immortal for the duration of the effect.