A "bad apple" is someone who might not be in trouble with the law (as is the case for "a bad egg"), but is a person who has a bad attitude (often about work), who is a negative influence in a team, and who is generally not pleasant to work with or be around.
Ex.: "That guy we just hired? I think he's a bad apple. He snaps at co-workers; he's becoming a real distraction." The new employee is creating negativity around him.
A Bad Egg
Figuratively, a bad egg is someone who is often involved in trouble, such as petty crime, vandalism, and so forth.
Ex.: "I don't want you hanging around with that boy! He's a bad egg. He'll get you arrested someday!" Here, "that boy" is well known as a delinquent and is involved with shady things (though not necessarily on a serious level... yet).