These things are horrid for hinge-related failure. Normally it's a combination of excessively tight hinges and weakening, poorly-engineered plastic mounts in the display housing, though occasionally the mount posts on the lower frame will snap off. You may be able to remove the name badges from the front of the display (the "Macintosh" and "PowerBook 3400c" ones) and VERY GENTLY tightening the screws beneath, though there are two more screws that are hidden under the bezel that may also be loose. It's more likely that the screw bosses have broken. You won't know unless you try to disassemble the display housing, but you're likely to totally destroy the thing in the process. It's no-win here.
If, however, your screen housing doesn't look deformed near the bottom or make horrible crunching noises in any way and is simply too easy when moving, I'd say leave it. Better with weak hinges and intact plastics than stiff hinges and shattered plastic.