The Cr-48 hinge design, specifically, where the metal hinge plates mount to the plastic case, is subject to fatigue and cracking, and failure is not a matter of IF but WHEN.
If you are willing to split the case, a pre-emptive repair is better than trying to put the broken bits back together after the fact. Epoxy (I used JB Weld, which is available at most hardware stores) can be used to reinforce the mounts. A slow-cure epoxy is better than the 5-minute stuff, because it gives you more time to work before it sets.
Before starting, see the Cr-48 Video Gallery repair video, so that you feel comfortable about opening the Cr-48 without damaging anything. Assuming you have a phillips screwdriver of the appropriate size, the most difficult part of the process is keeping track of all the little screws -- there are at least three types (long black, short black, and chrome). Pieces of masking tape on the work surface allow you to stick each screw in its relative location as you remove them.
With the bottom of the computer removed, remove the hinge plate screws, flip up the hinge plates, mix a batch of epoxy, and carefully spread it around the hinge mounts. A chopstick or wooden coffee stirrer makes a good tool for this purpose. After spreading the epoxy around the hinge mounts, screw the hinge plates back in place, and check that the still-liquid epoxy isn't flowing into areas where you don't want it to go. Then, close the screen, check alignment and, if necessary, use some masking tape to hold everything in place while the epoxy sets. Typically, JB Weld starts to set in about 30 minutes, but it needs 12-24 hours to reach full strength.

Left hinge mount

Right hinge mount

When the epoxy is fully cured, put the case back together, and stop worrying about broken hinge mounts!

Related wiki: Lid Alignment