You've got every right to be pissed. Even though you'll not starve, it's showing you from the gitgo that this is a sloppy organization, and you can expect more of the same.
Of course once you're aware and have lower expectations of normal business practice, the job may work out to be tolerable anyway. You may even be able to use the sloppiness to your advantage.
You mentioned they've been around since the 50's, probably momentum and habit prevents crash and burn.
Talk to your boss about hiring Monster to kick ass and take names.