We recently had a problem with a Java server application where the application was throwing Errors which were not caught because Error is a separate subclass of Throwable an
It all depends a bit on what you're going to do with an Error once you've caught it. In general, catching Errors probably shouldn't be seen as part of your "normal" exception flow. If you do catch one, you shouldn't be thinking about "carrying on as though nothing has happened", because the JVM (and various libraries) will use Errors as a way of signalling that "something really serious has happened and we need to shut down as soon as possible". In general, it's best to listen to them when they're telling you the end is nigh.
Another issue is that the recoverability or not from an Error may depend on the particular virtual machine, which is something you may or not have control over.
That said, there are a few corner cases where it is safe and/or desirable to catch Errors, or at least certain subclasses:
So the bottom line is: if you do catch Throwable/Error rather than Exception, it should be a well-defined case where you know you're "doing something special".
Edit: Possibly this is obvious, but I forgot to say that in practice, the JVM might not actually invoke your catch clause on an Error. I've definitely seen Hotspot glibly gloss over attempts to catch certain OutOfMemoryErrors and NoClassDefFoundError.