They export correctly for me with or without any modifiers.

There is, or was, someone working on an extension to the Tools which added support for SFM-specific animation data. But the core tools themselves don't support that.

This issues has now been properly fixed. You'll need to get the latest version of the Tools and also upgrade to Blender 2.74.

You should find that fixed in the new branch.

If you need this fixed now, here's a temporary branch that doesn't export corrective normals at all[github.com].

This is an issue with corrective shape key normals. Looking at Valve's files, many corrective normals are as short as 0.01 units, instead of the expected length of 1.0.

I'll ping someone at Valve and ask what's going on.

This is almost certainly down to the fact that I added the export of shape key normals. Before then the normals didn't change at all. It's purely a lighting issue; the verts and UVs stay correct. I'll look into it.

What do you mean by "export compatible"?

This will be fixed in the next release. You can get the fix on GitHub if you need it sooner.[github.com] You'll need to use Blender 2.74 though.

Don't use release candidates.

Having multiple armatures on the same exportable is unsupported, as it allows behaviours that Source doesn't support and also opens up all sorts of complications with regard to bone names etc.

The bug was that this wasn't detected between grouped objects. Now you will receive a user-friendly warning when you try to export your scene.

To fix this, use one Armature for everything. By using bone layers and groups you should be able to achieve everything you need with one object.

You can still have whatever parenting system you want...just don't use Armatures for it. :)