**Caveat** I'm a heroic raider, playing for 6 years, who uses LFR to hit my VP cap, to get the odd piece I need, practice a new spec, test new gearing, or at the start of a tier to get a gear edge. I am someone who has the time and desire to commit to a raid schedule, so I'm certainly not the designed audience for LFR, specially with the advent of FLEX. That being said, I love the idea of LFR and how its been implemented. I'm sure it has achieved its goal of broadening the audience of people who are raiding and getting to experience the content.
Obviously everyone knows LFR can be tedious and full of a few squeaky wheels. Queues can take forever and there is always the few players who are purposefully or accidentally making the experience negative for others. On the contrary there are times where it goes smooth and works as intended. There are tons of posts (just | like | here) that blame LFR for how LFR is and the "decline" of the current WoW masses and how "less skilled players have become". There is no shortage of LFR hatred out there and much of it is from personal experiences so its difficult to argue what others didn't experience (although its the internet, so there is always those who try).
I personally haven't noticed a drop in the skill of the players, its that the Normal, Heroic, Casual, Elite, whatever, players are being mixed much more now than they were in past expansions so the disparity between the "LFR" raiders and the "Normal" raiders is much more evident. In the times before LFR you were either a Heroic or Normal or Non raider, Hard Modes or Normal Modes raiders, Black Temple or Kara raiders. Now we added LFR so that more people are getting involved in raiding, which is their point. It has had the unfortunate side effect that the "Normal" raiders have been looking down on the "LFR" ones much like the "Heroic" raiders of the past looked down on the "Normal" or "Non" raiders. The insult has moved from "Well, you've never even killed the end boss" to "Well, you've never even killed the end boss on Normal". I haven't noticed as much "Heroic" vs "Normal" elitism or insulting as it was in BC, Wrath, etc. it has moved to "Raiders" vs "Players who raid".
Less Skilled Masses
Like I said above, I haven't noticed an overall drop in the skill of the players, just that there are more players that I come into contact with through LFR that I wouldn't otherwise get to raid next to. I do however have an alternative answer to any belief that the skill of the players is declining.
I saw a marked change in the skill of players at max level with the advent of Refer-A-Friend, Heirloom gear, and the decrease in XP required to level. In my opinion this makes sense. I learned how to play my character by leveling them up, by questing, through dungeons, back when things like EJ were just beginning. Did I hit max level having mastered my class? Absolutely not, but I had a general idea. With the ability to level 3x as fast with RAF or 45% faster (?) with Heirloom gear, combined with less XP needed there is much less time for new players or players new to a class to learn the ins and outs of the class. *Hyperbole approaching: If you're getting 10 new levels every hour and a new spell every 5 levels, why would you take the time to learn what the new things do when the previous things got you there.* With the decreased time required to level there is decreased opportunity and time to learn what should be learned to make the most out of ones class at max level. New players gifted levels or carried by RAF friends are given a toolbox full of abilities that they've never had the reason to use and then yelled at for not knowing what they all do.
I also feel that the LFD function, more so than LFR, attributes to less knowledge of a class for players new to the game or to a class. If you can level to max through dungeons as a DPS, there isn't any instances of where you have to do the most damage as possible to kill the target before it kills you, you have a tank to do that, so any DPS you do will speed it up, but rarely effects the eventual outcome. Tanks don't often have to learn how to keep themselves alive or kill a target before it kills them because there are DPS to kill it for them, and healers to keep them alive. Healers learn how to heal, I have little problem with dungeon-ing as a healer as it teaches you exactly how to do what you need, to a certain degree, and its hard to learn how to heal while you're trying to kill the quest mob.
Don't get me wrong, I love having to spend less time leveling a toon, but I'm the kind of player who researches the best rotation and spec for leveling and I fill the skills into the rotation as I learn them. For someone who isn't as thorough or is new to the game, there isn't the same need or opportunity to learn new skills and the nuances of the class.
TLDR; Poor LFRs and "bad" players are just a symptom of a problem that is the side-effect of Quality of Life improvements made to the game that have overall made the game better.