One of the most common ones is the idea that WOW is entirely twitch reflex based and not strategic. Tobold and Gevlon, among others, seem to have this idea that as long as you click fast in WOW you are going to be awesome because nothing else matters. I just don't see how that makes the slightest bit of sense. Clearly when playing a fast moving game you have to make rapid decisions but strategy comes up all the time. Healers moreso than others need to be monitoring their mana and their casting patterns to find more efficient ways to keep the group alive. That said, everyone has cooldowns to use and things they have to choose timing on and figuring out when to do that is important. Regularly when my guild was tackling hard content we sat down and had discussions about how many DPS to put on a task, which ones, and who would take special jobs. Clearly at the end of the day you are going to have to click a bunch of buttons really quickly but there was huge amounts of time devoted to strategy and people who couldn't plan ahead were obvious because they failed at their tasks.
Although much of the button pressing thinking is offloaded to mods these days I don't know that this removes the strategic element to hitting abilities. I spent hundreds of hours building and maintaining my spreadsheet to tell me exactly how to play optimally and many of the choices that ended up being the best were not at all obvious from the outset. Though it is true that the average player usually does simply download the appropriate mod and accept whatever the theorycrafters say I would point out how often my theorycraft slightly differed from others and that these small differences were relevant. Doing the theory myself was important and gave me a real advantage over those who just went with whatever they found online. I suspect that much of the complaints of WOW being all twitch based come from people who simply never did much hard content. If you are doing easymodes you rarely get pushed to the limit of your potential - as long as you can do 80% of the optimum you will win as long as you don't stand in the fire. When you do hardmodes with minimal gear though you end up being forced to never stand in the fire and also deliver 95% of optimum and doing that requires a ton of information, strategy and thought to achieve.
The second big complaint I see is that you don't get to use your class abilities as you raid. I totally get this one as I recall vividly going into AQ40 back in the Classic days and being awed that I had to actually Hammer of Justice things. No monster in the preceding dungeons was affected by anything aside from autoattack so I really only needed 3 buttons on my bar - Flash of Light, Holy Light and Cleanse. In AQ40 not only *could* you use all kinds of 'levelling' abilities you *had* to use them or you would die. There was a huge increase in the number of abilities you needed to use to be effective and I thought it made the game a lot more fun. In modern raiding this still holds true - I loved fights where the monsters were brutal but could be slowed, interrupted, stunned, etc. and we had to use all kinds of crazy tactics and spells to solve problems. I remember really enjoying the challenge of piecing together how we would solve particular problems with the raid members on hand and having to be aware of all the neat things stuffed away in our spellbooks.
I think the raid design team is doing a MUCH better job than they used to at incorporating more class abilities into fights which I find pretty hilarious when I compare it to Tobold's recollection that BWL was the best zone ever for forcing him to use his abilities. The BWL I recall was one where mostly everyone stood in one spot casting either Fireball, Frostbolt, or their single most efficient heal. Nothing came out of your spellbook aside from the 3 basic things you needed to do - there is no question that modern fights require far more in terms of skill, output, flexibility and using all of your abilities than the ones in BWL did.
WOW isn't perfect, as is evidenced by the fact that I don't play it anymore. However, there has been a major improvement in making use of levelling abilities in endgame and the level of strategy required for the challenging encounters is extremely high. You *can* get by with minimal strategy and you *can* ignore your spellbook but only if you are doing easy stuff. If you want a challenge, it is there... and if you don't agree with me I want to see your list of heroic mode final boss kills that were done before the boss was nerfed!