Can I set my DVD player on its side, in my bookshelf, and expect it to work?
Only if it has a mechanism to keep the DVD seated in the tray when vertical. If you have tabs on the tray, or a spindle to click into the drive, it should be fine (the PS2, for instance, can operate vertically). However, if it Doesn’t have a mechanism for securing the disc vertically, then I wouldn’t try it. You risk having the disk rattle around and get jammed before the spindle in the player can clamp onto the disk.