Some observations about negative aspects of SCRUM in my experience:
A misleading sense of detail.
There are so many specific process details in SCRUM that it's very easy to get mired in process while losing track of the high level goals (and then it becomes just a cargo cult process). Also, SCRUM generates a lot of artifacts, it's easy to mislead yourself into believing that this plethora of data gives you more visibility into the development process than it actually does, and the sheer quantity of data probably discourages people from asking whether they're getting the right information.
Over application.
SCRUM is often mis-applied as a general purpose fix-all process for every situation when, like any process, it only has usefulness within a fairly narrow set of circumstances.
Pressure for short-sightedness
SCRUM encourages short-term work on concretely defined tasks. Less well-defined work (especially work that doesn't have artifacts already existing in the system) like research or strategic planning is at a disadvantage in getting developer time.
Misplaced credit
SCRUM is one of the most visible development processes, it helps that it has a catchy name/brand, which means that often a successful project that uses SCRUM is more likely to result in SCRUM receiving a good amount of the credit than a successful project that employs a development process which is less noticeable and doesn't have such a catchy name.
FUD
Those most trained in SCRUM seem to be the most blindly defensive of it, going so far as to try to scare people into thinking that even the slightest deviation from the one-true-SCRUM-way leads to the dreaded "waterfall" process. Given the enormous multiplicity of different development processes, many of them with plenty of good qualities all their own, this tendency is pretty ridiculous. Also, there is this idea that the only way to be agile is to use SCRUM(TM) or TDD(TM) or XP(TM), when in reality there are many ways to achieve development agility without any of these specific methodologies. The truth is that no development process is a silver bullet, and the best development processes are really only incrementally better than the 2nd, 3rd, etc. best processes.