Security is about creating layers of defense, with redundancy if possible.
Excellent points, but I would like to add a few more.
1) Most sliding windows can be lifted out of their frames and the casement locks that come with them are typically weak enough to pop with a flat prybar. Since it's a rental, I doubt permanent alterations are allowed. You can use foam tape to hold blocks in place for the same purpose. Back up the original locks with wood dowels.
http://www.command.com/wps/portal/3M/en_...Vbe7NZP56G6BDgl2) Buy a decent confetti shredder and use it. No matter what apartment complex I lived in somebody would always go through the trash. I kept finding envelopes that I had thrown out lying on the ground next to the recycling bin. Your identity can be stolen and sold, and it can be VERY expensive for you. If it has your name and adress on it, it get's destroyed. Also consider moving documents off site into a safe deposite box.
3) The same goes for computer data. Encrypt anything else that can be used for identity theft.
4) No idea how to reinforce the door without permanent modifications. Material for convincing the apartment manager is below.
http://www.thenationallocksmith.com/public.asp?2EDIT
The reason I wanted to go with wireless is that I'm assuming that the doors and windows won't do any good. I'm also re-thinking because I'm sure that the opportunistic criminals would be the ones going after the electronics, NOT the really "cool" stuff like identity paperwork ( i.e. birth certificates, passports, social security card, etc. ).
Wanna bet!?! The last time my car was broken into, the theft of my personal papers cost me many times that of replacing the window and radio. Even after adding onto what the insurance covered.