The problem is that the hinge gets stiff over time, but it's really flimsy, and you naturally want to push the lid open by shoving the top of the display, which puts a lot of torque on the hinge. It either snaps in two or breaks free from the lid (it's glued on). Lubricating it is awkward because there isn't much space for the lubrication to spread.
It wouldn't be so bad if the hinges were easy to replace, but they have to be epoxied in place, and they're long out of production. It's frustrating because the oldest laptop I still occasionally use - a ThinkPad 600X from 1999 - still has a fantastic hinge that's loose enough to open with one finger but stiff enough to remain in place even when the machine is turned upside down. The TiBook hinge wasn't Apple's finest moment. The irony is that it doesn't even look stylish, it's just an awkward design presumably brought on by a desire to put all the ports along the back of the laptop so that you didn't have to look at the cables.
Beyond that my understanding is that the G4 iBooks had a poor reliability record - over time thermal cycling caused the GPU solder joints to break, at which point the video failed. There were home-made fixes that involved baking the motherboard in an oven or using a heat gun on the GPU to reflow the older. A similar problem affected the PlayStation 3 and xBox 360. In the case of the iBook it was exacerbated by the difficulty of dismantling the machine.
In Apple's defence faulty GPUs were endemic in the world of PC laptops as well. Back in 2010 Dell settled a class action lawsuit because lots of their notebooks with NVidia GPUs overheated and died:
Off the top of my head the problem was that (a) the chip naturally ran hot (b) the cooling system looked something like this, with a combined cooling system for the CPU and GPU:
But the BIOS only monitored the temperature of the CPU, so if you played games or watched HD video the GPU ended up running way hot all the time.