Wiktionary
n. (context idiomatic English) Someone whose behaviour is reprehensible or irresponsible; a rogue
WordNet
n. (old-fashioned slang) a bad person [ant: good egg]
Wikipedia
Bad egg is a children's playground ball game played in Great Britain and other countries.
One player is chosen as the 'Bad Egg' and turns their back to the other players. 'Bad Egg' then asks the others to each name something from a particular group (for example, each player is to name a colour, or a sports team, etc.). Once each player has answered, the 'Bad Egg' throws a tennis ball over their shoulder, and shouts out one of the answers that had been given by the other players. All players, except 'Bad Egg', run in different directions and the person whose answer was shouted out has to run after the ball, and calls "stop" when they retrieve it.
On hearing the word "stop," all players, including the one who went after the ball, remain stationary. All players, except the one with the ball, stand with their legs apart. The player with the ball then attempts to roll it under the legs of one of the other players. If successful, that player becomes 'Bad Egg'. If unsuccessful, the player who retrieved the ball becomes 'Bad Egg'.
Usage examples of "bad egg".
Rather bright and so forth, but in its proper place not altogether a bad egg.
Without really intending to, as he let it slide from hand to hand, Peter dropped the egg on the rocks and with a tremendous bang it exploded, filling the air with smoke, fire and brimstone, for it was, as Roger had hinted, a very bad egg indeed.
Trouble with Mort the Wart was that he was not a bad egg, nothing to hate about him other than fact he was symbol of Authority.