A simple question. I know that non-manifold meshes are problematic for physics simulations, boolean operations, and 3D printing. I was wondering if they can be problematic for a virtual reality environment as well.
No, VR is no different to flat graphics applications in this respect. If your VR experience has physics, CSG (Boolean geometry), or any of the things that would have problems with non-manifolds in a flat application, then it'll have the same problems. If your application wouldn't have problems with non-manifolds as a flat application, it won't have problems as a VR application.
The only real difference is that it's harder to stop the camera being inside objects in VR, since it's attached to the user's head. In a flat application, you might override the camera position or adjust the camera controls to avoid the camera moving through objects in the first place. In VR, those techniques don't really apply, so you might want to have an inside-outside test, so that you can react if the user puts their head inside an object (e.g. by blanking the view completely and/or asking them to move). The inside-outside test would obviously have problems with non-manifolds. It's the same problem as in a flat application, but in a flat application you might not be doing the test at all.