Basically, it looks like Bethesda did some stealth editing of the Dragur references (which wasn't mentioned in the patch notes), why? Who knows. But any mod that tinkers with Draugr-related crafting stuffs now causes the menus to disappear due to that. Here's a temporary workaround, basically you're just removing the Draugr references until the mod authors in question can release official updates (hopefully this will help them, as people will stop complaining about this so much, since it isn't their fault, after all).
Note, this is only relevant if you use crafting mods with Skyrim.
Instructions
1. Download FOMM from fallout3nexus.com and install it.
3. Open notepad and save a file as Fallout3.exe (not Fallout3.exe.txt, you need to be careful about that).
3. Put the fake executable in the FOMM folder, or some other folder you know the path to and of.
4. Open FOMM.
5. Tell FOMM that you wish to use it with Fallout 3.
6. Point it at the directory that contains your fake Fallout3.exe file.
7. It'll have a bunch of error messages, just click through them.
8. Click Tools.
9. Click TESSnip.
10. Do the open file thing.
11. Navigate to your Skyrim Data folder, this is where you extract your ESP files to.
12. Pick a crafting mod, and open it.
13. You'll notice on the left that there are one or more trees available now, expand them.
14. Look for any entries that include the word 'Draugr' and delete them (use the delete key with them selected).
15. Save and close the file.
16. Repeat steps 10 to 15 for every crafting mod you have. If you don't find Draugr in a particular crafting mod then don't worry, that just means it's already clean.
17. Start Skyrim, your missing menu woes are now over!
FAQ
Q: Where is my Skyrim Data folder?
A: Look for your Steam folder, it should be in either in C:\Program Files or C:\Program Files (x86) unless you installed Steam somewhere else (in which case you'll probably be able to figure that part out!). From there, you go through SteamApps, Common, Skyrim, and then Data. So the full path should look like this: C:\Program Files\Steam\SteamApps\Common\Skyrim\Data (Do note: This may not be exactly the path for you, so find it for yourself if that doesn't work.)
Q: How do I create the fake executable?
A: Open notepad, with the text file blank, just use Save As. Enter the filename as Fallout3.exe, then check the file you've saved and make sure it's named Fallout3.exe and not Fallout3.exe.txt. You may need extensions visible to check this, if you don't have file extensions showing, there are a number of guides online. Just search for 'windows show file extensions guide' and you'll be fine. Remember, the file has to be Fallout3.exe, not Fallout3.exe.txt. Otherwise it won't work. Then, like I said, just put it in a path you know. You can even put it in the Skyrim path you discovered above, if you like, if that makes things easier. It doesn't really matter.
Q: How do I open a crafting mod?
A: Once you have the open dialogue looking in the correct folder (just plop the Skyrim Data path you found into the path field and hit enter), you just pick a mod. It'll be showing ESP files, so it shouldn't be too hard to figure out. One example would be 'Lost Art of the Blacksmith.esp' - you'd click that and then click Open. Simples!
Q: I've run into issues/random FOMM problems. Help!
A: I know that's not a question, but I suspect this may be a thing. If you do run into issues, it might be due to Vista/7's security measures. What you'll want to do here is right-click FOMM and select to run it in Administrator mode. You'll find that in the context menu easily enough. Just launch FOMM that way and you should be fine.
That should about cover everything!