If a device such as this potentiometer has a metal case, should the case be grounded or left floating? Electrically the case is not connected. Data sheet
Floating pieces of metal are mostly unwanted. The reason is that they have an high impedance to the environment and can pick up noise and then induce noise to you circuit.
By connecting it to your ground plane the noise will flow a defined path to your ground instead of some sensitive circuit nearby.
BUT: Be aware that these components usually stick out of your enclosure. An esd discharge path is also created to your ground. If you have a metal enclosure connect it directly to the enclosure and prevent the discharge going via your pcb. If esd is a high risk and you have a plastic enclosure, make sure you add proper esd suppression. Isolating this piece of metal by not connecting it to anything is almost impossible because of the pins nearby (small spark gap).