Some holes and incosistencies aside (like Donald and Goofy not recognizing the Mysterious Tower in KH2) I find the story of the KH series fascinating on paper and it really does have its moments but I think the real issue at times is how the story is told.
Too many times it is tell instead of show, often with unneeded exposition that could have been told more effectively in a cutscene or something. For example, I really disliked how in KH2 it was Yen Sid who goes on a long explanation about who Nobodies and OrgXIII is instead of introducing them to Sora in a more meaningful way.
Also, often times it's like they are confused for who the story is and how they should write it. In some games, the dialogue can be written in a very good, meaningful way (look at the BBS secret ending for example) but the second it goes to a friendship speech of how "My friends are my power" my eye sockets can barely contain my eyes. Like, there are a lot of ways to convey the sentiment of friendship that is not that obnoxious and barf inducing. It goes from complex to basic from one scene to the other.
"Alright, we have a dark tale about murder, illegal experiments, idenitity theft and a war that ravaged the entire known world... Oh wait, I forgot we have to market it to 5 years olds too."