As a huge fan of the Diablo series and ARPGs in general, I personally love Diablo 3 quite a bit. Yes, Diablo 2 and 3 are quite different, but they are both fun in their own ways. Disregarding the always online requirement, which obviously sucks, I still cannot really grasp the amount of hate the game has received. I understand a lot of people just aren't fond of it and that is reasonable, but the outright hatred for it seems a bit odd.
Although it has received a lot of complaints, I actually prefer the current method when it comes to unlocking skills. I enjoy unlocking all the options available to me, and not getting halfway through the game and realizing I made a mistake and have no real way to fix it without starting over again. I enjoy being able to constantly experiment and find good synergies with friends who play different characters. I enjoy not being locked into any one specific build. I almost always play a monk, which is incredibly versatile, and it is fun adjusting my role between high dps, healer, tank, or whatever the group needs based on their builds and experience level.
Another complaint I have seen a lot of is similar to the above, but regarding attribute points rather than skill points. This problem is pretty tricky, as I see a lot of people talking about how you only ever focus on one attribute and nothing else for your characters. Yes, all the characters are usually driven by one attribute when it comes to damage, but if you play on hardcore mode where this game truly shines, you will see the need to focus on all attributes accordingly. It is one of the reasons I actually enjoy changing my character through gear instead of a permanent point system. I can constantly experiment, and I am not stuck putting hours into a character that will eventually be gimped and useless in later difficulties, forcing me to start over.
Although it doesn't help the current situation, at least they are bringing attribute points back in their next major update through the paragon system, so hopefully that will provide the best of both worlds and make both parties a bit more happy.
As for other things, such as the story and all, I agree that is less than entertaining. After the first playthrough though, that is honestly something I just tune out and skip through completely, as my only focus is the enjoyment of smashing demons and hoping for fun loot while blasting whatever music I enjoy through my headphones. This pretty much goes for how I play all ARPGs.
The auction house aspect also sucks, but I never found it quite as detrimental as people made it out to be. As I previously mentioned, I only play the game on hardcore mode, and there the RMAH doesn't exist. A basic gold AH exists, and I have only occasionally made use of it. I do wish more fun things dropped on their own (and surely it will when Loot 2.0 comes into play), but the game is still manageable by avoiding the AH entirely.
And finally, as a suggestion to those that are willing to give the game a try, I thoroughly suggest hardcore mode. This isn't for bragging rights or feeling like a badass, but simply because it is a lot more exciting. I have yet to finish the game on inferno mode this way (only 1.5 acts away though!), but it really forces you to learn the game, pay attention, and find what works for your character. What works in softcore mode does not always work in hardcore. I often see people just throwing themselves at enemies with the most DPS possible and randomly dying, rinse and repeat. In hardcore though, you need to build a balanced character and focus on multiple aspects. I do have a softcore character I poke around with on lower levels occasionally, but it really feels lacking in terms of excitement now.
Anyway, in summary, the game is far from perfect. If you go into it with an open mind though, I think it can be fun in its own way. It does a lot of things differently, some of which I have found fairly enjoyable. I find both D2 and D3 fun in very different ways, and I plan on continuing to play both depending on the mood I'm in.