I found a couple of things on the internet mentioning this problem. In my PowerBook 520c it manifested itself by causing the plastic cover over the back of the screen to catch on the plate underneath it when opening the PowerBook. I found that by tightening the plastic screws that connect the metal hinge into the screen cover this became less of a problem, but I still put twine tape over the back piece and microphone cover to make this joint travel smoothly over the part underneath. The screws required tightening every few months and the tape had to be replaced. I also noticed the PowerBook didn't latch very easily which was probably due to the deflection of the screen as the screws were pulling out. On about the third time I was going to tighten the screws I noticed that the flanges from the bezel around the front of the screen had cracked and the post underneath one of the hinges was cracked all the way around. I suspect part of this was due to me tightening the screws too much, but mostly it was just a bad design originally. There is a very strong steel hinge anchored into the screen via these plastic posts. It just makes sense that the plastic post will lose the battle with the steel hinge.
One suggested repair involved cutting out an L-shaped aluminum plate and attaching it to the back of the screen via bolts passing through the plastic posts (which had been drilled out) then the hinge, then the screen bezel flange and finally a washer. This is what I planned on doing once I found the cracked post. The guy who posted this to the Web originally has disappeared, so completely without his permission, you can check out his original instructions here. Even if you don't use his method of repair, it is a good reference.
What I wound up doing was a less exhaustive repair than described above. I found that only one post was severely damaged and machining an L-shaped aluminum plate was really beyond my capabilities and patience. Instead of the plate I used a big washer on the back of the screen and instead of replacing all four screws connecting the two hinges to the screen, replaced one screw of one of the hinges (the left one).
I took apart the PowerBook and removed the screen from the base. The post in question had already come apart, leaving only the bottom half of the post. I drilled a 3/16" hole from the center of the base of the post through the back of the screen. This size hole will fit tightly around the bolt you will use, but not so tight that it won't slip a little. Unlike the original system of screws being threaded into the plastic, the bolt will do its work by pulling everything between the bolt head and nut together, so everything in between needs to be able to slip and become snug against the adjacent pieces.
I then built up this whole section using some stuff called Power Poxy, a plastic epoxy that becomes rock hard overnight. It's nice because it lets you mix about a quarter of an ounce at a time which should be more than you need. While the epoxy was still soft I covered the back of the hinge plate in oil and pressed it onto the epoxy in it's final position. This is critical, as you will never be able to fit everything back together if the hinge doesn't wind up where it needs to go. Also, putting in too little epoxy won't give you the bearing surface you need to transfer the load from the hinge to the back of screen plate. Make sure the impression is pushed in at the right place and make sure the epoxy doesn't stick to the hinge (thus the oil). Remove the hinge and let the epoxy set up.
The hinge had some little tiny steel apparatus clipped to it that had an arm that went over the end of the hinge. This kept falling off so I superglued the flat part of it to the hinge.
Fig. 1: Exploded view of bolt assembly
After the epoxy was hardened I drilled back up from the back of the screen and through the epoxy, which effectively left me with one giant plastic post instead of the pathetic tiny post Apple had used. I then got a #4-40 x 1" machine bolt (I needed to cut 7 mm off of the end of the bolt), put a 1/8& x 1" fender washer on it and ran the bolt through the back of the screen. This bolt then passed through the hinge and up through the flange of the screen bezel. I decided to install a washer on this end and used a #6 Cut Washer whose edges I had to file flat in order to make the round washer fit in the square flange area. Since the flange was already cracked I decided to Super Glue the washer into place on the flange, hoping that the washer will hold the flange together. Even though I wasn't fixing the hinge on the right, I did the same thing to the flange on that side that was cracked. I put on the nut snugly and then screwed all the old screws into place. Then I really tightened the bolt down tight. The end of the bolt stuck up a couple of millimeters from the nut so maybe I could have shortened the bolt a little more. After I put the PowerBook back together I went ahead and put tape back in place. I might have been able to do without the tape except that I broke the little tabs that keep the microphone cover in place so it would just fall off otherwise.
Fig. 2: Completed bolt assembly
My hope is the load from the hinge as you open and close the PowerBook will be transferred into the epoxy and ultimately carried by the bolt. The big fender washer on the back should distribute the load over the back cover of the case. I think maybe a ¾" washer might have been more appropriate since the edge of the washer hangs over the bottom of the back screen cover where it starts to curve. After about two years it is still working better than it did before the repair.
What you will need:
3/16 bit for drill
Torx 8 screwdriver (available at Sears)
Butter knife, guitar pick, or credit card to remove screen bezel
File (or pliers and a sanding block) to file washers into square shape
1/8" x 1" Fender Washer (3/4" will do)
#4-40 x 1" Round Head Machine Screw with nut
#6 Cut Washer
All of this is available from a hardware store (I got everything I needed at Home Depot). Write to me if you have any comments or want more information.