You probably don’t want to read this, unless you got here by googling the error message. Just a bug workaround, which I’ve backdated into the archives so it gets to exist somewhere online.
The problem: Most websites which use localstorage stop working. You look in the console, and find many errors NS_ERROR_FILE_NO_DEVICE_SPACE. But there is plenty of space on your hard drive
The solution: delete storage.sqlite in the firefox profile directory
What’s going on: the sqlite database that manages localstorage got corrupted (perhaps because the disk was full at some point). Delete the database and firefox will happily recreate it.
…At least, that’s what worked for me. No guarantees!