alt Hacker NewsThere are mirrors in Picard and Troi's quarters (click the viewpoints near the beds), and I think you can catch a glimpse of the camera they used to make the panoramas. It's blurry, and kind of looks like a droid from Star Wars.
I suppose it's also possible they photoshopped in something that looked sci-fi, to cover up whatever mundane camera they were actually using.
If I remember correctly, the VR setups of the time required fisheye lenses attached to DSLRs and multiple shots. The thing visible in the mirrors are probably edited in.