George is right. Both are used. In the first sentence the "me" is implied you assume that the person asking is the one who wants the salt. However, people often say me anyway.

Actually, you could use both. I use both.

"pass" means to move from one place to another. It is either moved to a person or is a person moving somewhere. For example, passing the salt to someone or a person passing from room to room. If someone asks "Could you pass the salt please?" then they are asking you to give it someone. We can guess that they want it, so don't need to add "me" after "pass", but maybe they want you to pass it to someone else. Without the pronoun, it is unclear.