In the picture below, you can see the hinges and the two screws on each one.
Are these the screws that you are talking about? If so, they only hold the hinges to the main chassis of the system. The hinges around the LCD (on the bezel) hold the LCD plastics in place and do not have anything to do with the hinge, so tightening them up won't help either.
Inside the bezel, the hinge is basically just a flat piece that moves with the panel. The more I read your descriptions and think about this, the more I think the problem is the hinge itself.
I did some checking, and while the hinge kit for the E1505 is available, for the I9300 the hinge is part of the LCD (hinge up display) kit. If your system is still in warranty and the hinge is a problem I definitely recommend contacting tech support as it is a relatively easy fix. If you are not in warranty, the hinges themselves are not that expensive (assuming they are available separate from the LCD panel).
Dell Customer Advocate
PS: Thanks again for posting the pic, f_v_man.