Honestly ... nothing, not a damn thing. I sit back and learn the job as it is done NOW by the people that are there. After some time and when you are sure you have a good handle on how things work now (not just technically, but politically, and inter-personally as well) you can start formulating lists of what you think should be changed.
If you don't understand where you are right now, your ideas of where you should be could and most likely will be wildly off from reality.
As for red flags:
- Many many manual processes
- No Change Control
- No Documentation or worse wrong documentation
- VP/C-levels that are WAY too involved in the day to day operations (like resetting servers when you aren't in the middle of an emergency and nobody else can do it)
- Cheap equipment everywhere but the company claims to make XXX (million/billion) a year
- Unhappy employees
- Constant firefighting
- No or poor monitoring system
- "You need to talk to 'joe'" is the answer to every question you ask
As for must haves ... I think that depends on on what you do and how you do things... like I must have a digi terminal server hooked to a modem with a dedicated line as a last resort if I can't get to my Voice Routers... but you may not need that. Once again, sit back and take some time to figure out how things are and what peoples complaints are first before swooping in and wanting to change everything.