I can say at least three:
- It takes a lot of time to keep the diagram reasonable and synchronized with the actual code. UML diagrams don't run, but require a lot of time. So they are good only if your organization size can manage them
- You cannot represent every condition in a sequence diagram. It's impossible if you want to deliver. So state diagrams should convey basic facts, not all the possible outcomes.
- Good UML software costs money and it takes some time to master properly.
So, I think UML is good as a complementary documentation role, and only if the size of your organization allows it.
Solutions... well, in the end, diagramming is just a way to convey high level information to another person, in space or time (e.g. could be you in some year time). Extreme Programming shifts the burden of information retrieval from dead tree to living brain. Of course, it assumes that the living brain never forgets, and never quits. Extreme programming uses redundancy to reduce the impact of such occurrences. In a large company, a strong layoff round could wipeout entire teams, so storing information into brains can be risky. On the other hand, large companies have human power to waste, hence the diagramming.
Also, as WDuffy points out, if you are a designer, and you have to communicate to a team of programmers what they have to implement, it's much easier to use a UML diagram. Of course, a small company with a small team has generally small goals, and you can organize people with a different style. A small company UMLing will only produce UML diagrams of their revolutionary product, and then it will be bankrupt.
UML is not good nor bad. It can be a good tool, but it must be used in the proper context.
Lacking features?
well, I found that UML is strongly aimed at an Object Oriented vision of the world. Our company mainly developed in python, with a strong focus on module level routines. Objects were lightweight data containers, but all the logic was done at the module level. It's difficult to properly model this implementation style at the UML level, unless you resort to some "hacks" in the terminology. I guess it's difficult to model in UML for functional or procedural languages.
Another thing I find annoying is the assumption of use case modeling as a diagram. My experience is that the best way to convey a use case is to write a short story or a short code tingling the feature you want to convey. The story should be short, one page maximum.
This approach has two advantages: if your story is a written prose, the Q/A team can read and test it easily. If your story is code, you can put it as a functional test and let it run during the night. A diagram does not satisfy any of these value added needs.