For Nissan's keyless entry, you have to be within a couple feet of the button for it to work. If someone is close enough to you at that point, you have issues regardless.
To start the car, the key has to be in the car. I've had my purse on the passenger seat and behind the driver seat without an issue, but sometimes the car will flash a little signal to say that it can't find the key & you have to move it closer. Once the car is started it's fine.
As for locking the key in- they thought of that, too! It will not lock if the key is inside the car or trunk. It'll throw a few quick beeps at you and refuses to lock or the trunk won't latch. That has saved my keys several times, back when I kept my laptop bag in the trunk (& purse in the laptop bag).
Ditto to Drolefille's comments about opening all the doors- one push to open just one door, two pushes to open all. There's a button on both the driver's side and passenger's side. One push to lock all the doors.
It's pretty much awesome