The advantage/disadvantage rules wound up being my favourite part of 5E. I like how it solves so many of the cumbersome rules discussions that tended to plague 3.5 and pathfinder (I´ve never played 4th btw). I also like how it is a tool I can use to give small temporary benefits or penalties on the fly. I also think it solves some of the balance issue from previous editions, though they are still present, and combat is much faster and more streamlined.
I dislike feats, and have done so since 3.0. I think, as a tool used to creature fun and interesting PC´s, feats are worse in 5E then later editions. If you solely used feats to optimise then 5E handles them better.
I really dislike the short rests as it severely interferes with my GM´ing style. If I´m going to use 5E in the future I´ll have to make a house rule that makes its easier to gain the benefits.
Most of the classes are/seem fun to play. The warlock tend to suffer from not getting short rests, its still a good class, but it gets boring when you only get to use one spell each and every time. I feel that the warlock is the only class that suffers from poor design, but thats maybe because I´m seeing more as a caster than as an alternative ranged warrior.
The warrior classes still doesn’t bring much, and they tend to get boring in the long run, perhaps with the exception of the battle master. And I don’t like the new wizard, without any metamagic, I prefer the sorcerer class.
There are some other major problems with the classes, like the beast master being horrible and the moon druid being too powerful (especially at early levels), but like I said the balance issues are nothing compared to 3.5/PF.
I like it as a d&d edition, perhaps the best one yet, maybe besides E6 versions of 3.5/PF. But as a GM I dislike it, it encourages optimization and gets slow and boring on higher levels, and the numerous sources of magic leaves me with fewer options to challenge my party. As a player I´m an optimizer when it comes to d&d, and would rather have the toolbox that 3.5/PF gives me to create fun and powerful characters.
I´ve never played an MMO (besides dark ages of camelot, once or twice), so I can't say whether it solves any problems associated with that