This post is more than 2 years old.
I try to keep track of what all the browsers add to their developer tools, but somehow I missed this. In a recent Firefox update, they finally added a "Storage" tab to the developer tools. For some reason, this tab was deselected in my Firefox. I only knew it existed when I opened up the options looking for something else.
Once added, and selected, you will then get the ability to view cookies, IndexedDB databases, and Local and Session Storage. (No WebSQL since Firefox doesn't support it.)
Expanding the IDB section, you can browse the structure of local databases:
And when you click an object store, you will see a list of data. If you click one row, you get details:
This will be very handy for folks working with local data. (And reminds me I need to give my presentation on this topic again!)
p.s. The title of this post says it was the "latest" Firefox that added this but honestly I may have missed it from an earlier update.