If this place is as dysfunctional as it seems, staying two weeks after giving notice will be a nightmare.
So clean your house now as you search for a new job. Take the time to get your work documented and tidied up. Do it quietly. Don't give any signals you're looking. Business as usual.
Once that's all set and you give notice, if your employer gives ANY friction at all then just walk out the door. If they need you for two more weeks of help they can hire you as a contractor at a nicely inflated rate.
And like chrisbennet says, schedule some downtime between jobs to decompress, unpack, and mentally prepare for the next gig (unless you really need the income).
That is normal for someone working below a Senior Developer, a manager, and some unknown portfolio of VP's, Executive VP's, and C-level staff. A person that far down the food chain doesn't have a medium size picture, let alone the large one...i.e. the perception that the company is dysfunctional is not based on business metrics but "how I've always done stuff before."
This is very true. That said, as a professional you need to act like one - even when your employers doesn't appreciate it. For example, the quality of a professionals [think doctor, fireman, teacher] work product isn't dictated by how much they are paid.
Find your next job. This is important: When your new employer asks you when you can start, tell them depending "on how fast your can wrap things up" 1 to 2 weeks.
If you current employer walks you out the door when you tell them you're leaving , enjoy a week or two off. If they want you to stay for 2 weeks you do that and start your new job afterwards.