The main thing you always see people have issues with is people rolling on items that they already have or have better than, rolling to trade for other items or to give to friends, winning two of the same items in one run, etc etc.
So, that being said. Something that might fix the issue is to make the loot in LFR similar to that of loot items that drop off Holiday bosses. They are unique making it so if you have the item anywhere in your inventory you automatically pass it. Now that wouldn't work for say the 1H weapons due to people duel wielding, though that would fix the issue of people rolling on items they already have for the sole purpose of trading, DEing, or just because they feel like it. That would also solve people winning more than one tier token of the same item in a raid because until that item was turned in for armor, they couldn't win another token for the same slot due to it also being unique.
Anyways, just wanted to throw out any suggestions to make LFR more enjoyable for those that play fair! :) Happy raiding.