I watched all the way to the end of the credits but the part where Zach's granddaughter says he just vanished was missing (you can read about it here http://www.gamefaqs.com/boards/943433-deadly-premonition-the-directors-cut/66138639 ). Is this a bug or do you need to do certain things during the game to "unlock" these quite important lines ?

They were there for me... but she says it when the credits start rolling, so you might've skipped it.
If you did watch the outro again, there is one more important post-credits sequence :)

What ?? But when the credits start her mother asks that she brings Zach his diner. Now I'm confused. And yeah I saw the last cutscene, "time to wake up" and everything. All the cutscenes with the granddaugther weren't part of the original game so it's kinda confusing. Makes it sound like he's back to being an FBI agent and these new scenes were some sort of dream ?

Deadly Premonition\updata\movie folder, add14_us.wmv :) It played after credits for me (not sure if it depends on anything you do during the game; I had 49 subquests completed, all cards, all races).
Loaded my save and, for some reason, this time it treated me with York's parents telling me that 'Sometimes we must purge things from this world...' (I was affraid they'll troll me and delete my save :)).
I guess those scenes take place long after Raincoat Killer investigation and York \ Zach are retired.

I also never got the "mom, grandpa's disappeared" bit.... I had to look at it with the add14_us.wmv file. I'm not sure if it's because I was missing a few cards or if it's just a software glitch.

I don't think it's related to the cards actually, as I've just seen a PC ending playthrough which did have the scene even though they were missing most of the side-quests. Oh well, I guess I may see it in-game one day, on a future computer. Or maybe on PS3.