To borrow a movie quote, LFR is usually something as follows. "You will never find a more wretched hive of scum and villainy. We must be cautious."
Between flamers, afkers, and people that give no shit...it can and usually ends up feeling more like a dentist visit then something resembling an "adventure through a difficult dungeon with exciting battles and rewards".
Since the main (if not only reason) LFR is run over and over is loot, a system needs to be put into place that determines whether or not loot will be received. As it stands now, you only have to be in the raid, and near the boss when it dies. That encourages people to lazy, find ways to die at the beginning of the fight so they can go watch TV or browse the web, not give a rats ass about their gear or performance, and for those that aren't the first 3, to feel genuine feelings of negativity towards players who do not pull their weight.
To combat all of the above, a system of checks must be put into LFR. Something along the lines of the following.
1. If <50% of a players gear is enchanted or gemmed, the only rewards they may receive from personal loot are special "enchants" and gems. These would only be active in LFR.
2. If a player does not dodge Boss abilities enough, their chance for loot should be lowered by a % based on how many times they were hit by an avoidable ability. (Think people standing in ground AoE on ...well, just about any fight). If a player reaches 0% , they receive a gray item worth 1 copper from their bag.
3. If a player does not reach a minimum threshold of damage/healing/mitigation on a fight, they will not be elgible for loot from that boss for the week. On ANY difficulty. See : All those people in your LFR doing 50-60k DPS on fights that are more or less tank and spank.
4. Players who actually regularly avoid abilities, perform well for their role (Damaging the boss, healing/dpsing as necessary, actively mitigating boss damage as a tank), should receive a token for a new vendor. Call it the LFR token. Such tokens would be able to be used to purchase special food/flasks/potions usable in LFR only , as well as warforged seals, and for enough of them, 1 piece of gear. (no exact numbers but something reasonable.)
While I'm sure there will still be some problems in LFR, there usually are, rewarding players based on performing the task properly and efficiently rather than just being there should a good amount of the issues LFR suffers from.
TL;DR: Blizz should implement a system that rewards actively doing the right thing and "punishes" players who expect to be carried.