Rather important, since it gives the product an alpha-quality feel. (How about sticking a "beta" label to it until it becomes a bit more polished?)
I've encountered the following situations where I did not get an even remotely accurate error message. Exceptions from third-party components should probably be caught on more reasonable levels (while the original exceptions would be still preserved in log):
Was attempting to upload a malformed CSV (well, it was not malformed, but had a separator different from ",". "Could not import CSV into database" could probably be sufficient.
Had an incorrect number of columns in one row of the CSV.
Issued a LoadCsv() for csv with mapping to date dimension before I called LoadDateDimension(). I got a NullPointerException, I think. "Could not map..." would be probably more appropriate.
Also, HTTP exceptions from the backend contain a printf()-like format string, with an argument list, maybe it would not be a bad idea to format it.