Tilting it is usually not the problem, it is the jolt that happens when you set it back.... There is really not much to see visually inside a PC. Fans spinning is about all you can see when a PC is operating normally.
As long as you don't slam it, there is no problem. The only moving parts are the fans and hard disks. The fans aren't that delicate and the hard disks are usually rated for over 50Gs of acceleration while running (this is quite a lot).
The real problem with moving the PC around while it is on is the risk of tripping it or disconnecting some cable you didn't realize was stretched out.