Hi I have another php related question

I just made a login system for my web - login.php, checklogin.php.. etc. I also have a lougout.php. Everything works fine (AFAIK) and what I want to know is how to solve this situation - someone forgot to click on logout when quiting the web? I think that this can be done by monitoring user activity on web. I mean update the time of last click on anything. And in checklogin then check if the time of a last click isn't too old.

If this solution is right - how can I see if user has click on something (there should be some http request every time a link is clicked, right?).
And the last question - what things should I pay attention to in this login system? I mean how can it be defeated, tricked, whatever...

Thanx