Sadly even some of the best shows have some pretty bad problems, most of which being either that the story is incomplete, or followup seasons aren't as good as the first season. There's also the rare, albeit not common problem of a show that has a really good story, but the animation is really bad, rarely is a story so good that it makes up for the corner cutting of animations but it happens.
I mean I guess if I was to name a few off my head, maybe even some semi recent ones, in no particular order i'd probably say, Kiseijuu, Mob Psycho, Hunter x Hunter 2011, and Inuyashiki.
Some honorable mentions, while I consider them to be good shows, these in my opinion might have problems either from having an incomplete story or being lackluster, bad followup seasons, or some other issue would be:
Darker than Black, Full Metal Alchemist Brotherhood, Tokyo Ghoul, Deadman Wonderland, Re:Zero, Death Note, Zankyou no Terror, My Hero Academia, One Punch Man, Sword Art Online, Death Parade, Saiki K, Made in Abyss, No Game No Life, Sexy Commando, and Jojo.
I have seen a lot more than this aswell, some I consider to be good aswell, but may not have as much substance as the shows I just mentioned above. There's so much fucking anime girl worship trash out there. Not to mention some dreadful animes where most of the show is just pointless talking, and not even good interesting or funny conversations either, but HAHA LE EPIC CUTE ANIME GIRL SO ITS FINE XDDD.