Hey there Korbearus,
First of all, machead is correct. In order to maintain the integrity of your Apple warranty, you should take the machine to a "certified" Apple care center.
That being said, tightening the display hinges is very simple. Aside from the 10 pentalobe screws holding the lower case in place, there is nothing in the way except for those rubber covers. They are held on with a mild adhesive and come off easily.