I've described some in the post I linked at the beginning, and many many others have described similar things. I've cribbed these from TJ Holowaychuk's recent post and added some others:

* callbacks are not logical for expressing sequential logic

* you end up with deeply nested code when having many sequential actions

* you may get duplicate callbacks

* you may not get a callback at all (lost in limbo)

* you may get out-of-band errors

* emitters may get multiple “error” events

* missing “error” events sends everything to hell

* often unsure what requires “error” handlers

* “error” handlers are very verbose

* callbacks suck

* too many different libraries to "fix" callbacks that each have their own problems

* e.g. easy to lose errors in Q promises

* varying performance of various promises/async libraries

* "best" async library constantly changes

* callback style is the only common api, so you end up with wrappers for each library x library combination

* sometimes forget whether a function uses a callback, returns a promise, is a generator, returns a stream, returns something that looks like a promise

* some libraries may not call callback asynchronously

and more. Callbacks have gotten a reputation as a dead horse that people like to beat on.