Opened milk lasts about 3 to 5 days in the fridge if you store it properly, but it really depends on how you keep it. Your friend is right about the door: it's the warmest spot in the fridge because it opens and closes constantly, and that speeds up bacterial growth. The best thing is to store it on the inside shelves, where the temperature is more stable and cold.
To make it last longer, seal the container well, avoid touching the mouth of the bottle or carton directly with your glass (use a clean one each time), and don't leave it out of the fridge longer than necessary. If you have milk that's been open for several days and you're not sure if it's still good, the easiest thing is to smell it: if it has a sour or weird smell, just toss it. And yeah, you don't need to obsess over it too much, but better safe than sorry.