When I changed my old HD to SSD on my laptop I simply couldn't unscrew the protective case out so I just installed without one. Its working just fine but I wonder if that is a problem. I'm referring to the metallic case that surrounds the 2.5 HD not the laptop plastic protector

As long as it's secure there shouldn't be a problem. If it could fall out or it is exposed, then that's not good.

What could be a problem is that the SSD would move up and down if I carried my laptop around. But I almost never do that, so maybe I shouldn't be worried