This is probably a dumb question, but twice in "Kara Para Aşk" I think I have heard "hoşça kal" said by the person staying behind. I thought the person leaving says "hoşça kal" and the person staying behind says "güle güle." Or is this a rule that can be broken? ... Teşekkürler!

Just like in English there are several ways to says goodbye. Both can say hoşçakal(ın) (polite form).

Only güle güle is just used by the person staying behind. 

See these for more explanation:

http://www.turkishclass.com/turkish_lesson_110

http://www.turkishlanguage.co.uk/greetingsbanana.htm

http://www.turkishclass.com/turkish_lesson_6

http://www.turkishclass.com/turkish_lesson_78

I guess I had missed completely that "hoşça kal" could be said by either person. It is only "güle güle" that is restricted. ... Çok teşekkür ederim!

You say ´hoşça kal´ for ´goodbye´ but literally translated it means ´stay happy´, ´stay cheerful´ so anyone can say it.

Hoş = pleasant, cheerful, lovely

Hoşlanmak = to like, to enjoy, to be pleased with