Sharepoint - Why don't Lists and Libraries show up in SharePoint Designer?

Having the same problem, I found a way.

First, I knew a list was broken, based on symptoms reported from other answers in this post (You should also check out this post, as it is quite informative). For one, alirobe's mentioning that /_vti_bin/ListData.svc isn't accessible if a list is broken.

When I went to "All Site Content", every list given there did work.

I couldn't discover which list it was that was broken, so in SPD, I went to "All Files" in Sharepoint Designer - which worked, even though many of the other Site Objects in "Navigation" didn't display anything.

I went through every list in "All Files" and used "Preview in Browser" on every one of them. Finally, I came to one that didn't open! Instead, it said,

feature d57f48.... for list template '100' is not installed in this farm...

So I deleted that list and everything began working again just fine in SPD.

There is a list of features here, by the way.

It was probably a problem with one of your lists or list templates. If you have a broken list, then it'll kill the listdata.svc page. See here: http://www.thorntontechnical.com/tech/sharepoint/sharepoint-designer-2010-listlibrary-there-are-no-items-to-show-in-this-view-listdata-svc-woes

I ended up deleting the broken subsite and creating a new one. The new subsite works correctly.