Never r un in a loot council oriented raid (most of my raiding has been 'serious casual' i.e. we want to do well, have standards, aren't oriented around heroics though because of time/RL stuff) but I'd imagine a huge issue would be agreement on what the goals of apportioning the loot are. If council isn't transparent about their criteria even if they're not corrupt it can appear that way.
SImple example - When player A shows, his DPS kicks ass and he's 20-30% above everyone else - but he's only there 60% of the time. When player B shows, his DPS is very good too but only about 80% of A's DPS. However, he is there every night. If council gives a drop to A, B could be upset and vice versa. Council has to be transparent about how much attendance counts vs raw performance, etc. If they aren't it will probably look like favoritism. And if they don't HAVE guidelines, but just hand it out on vague criteria they might not be corrupt but they will end up being subjective... and subjectivity is the biggest thing a loot system needs to kill off.
I got shafted pretty hard on Ji'kun loot distribution. I was on my Fury Warrior and my 2nd trinket was really bad, LFR haste bullshit. Fabled feather of Ji'kun drops, which is a huge upgrade for me, (it's pretty high ranked for Fury Warriors still even considering SoO trinkets) Death Knight officer needs it because he says he wants to try out Unholy but he never did ;P