Does anyone know how to tighten the hinge on this?

Hi, I am having this issue as well. Could you tell me how you removed the cover?

I have the XPS 15, which is built very similarly. I'm also having this issue. You need a small set of torx screwdrivers to open up the back. I found a good set on amazon a while back for around $5 I think

The trick is to find the screw under the service tag flap

Anyone tried isasukexd's answer and still have this wobble?

The dell XPS is famous for the loose hinge, then. My XPS L321X (2012) also have the issue.

Yes, the brackets under the backplate (screwed onto the chassis) can be loose, but it's not that loose. The screw that is the loosest is the one on the display.

How to tighten that?

First, open up the cover (like you are using it)

Use your fingers, pinch the top and bottom sides of the plastic part (on the screen). Then pull toward you. (away from the screen). A plastic tab on top should reveal.

Close the screen (like you are done using it). Use your hands, gently lift up the plastic part. Antennas should be connected to it. The screws are Philips white (can be black) ones behind the display cable and the antenna.