Much of this information was found here, at VCF member DeltaDon's old site.
The top display housing on the black J4s is rubber-coated. This coating was not nearly as high quality as the coating on ThinkPad laptops, and at this point will have gone sticky on all units. The issue was even brought up all the way back in 2005 on the page linked above. The rubber will have to removed from any black J4. The white/silver cased J4s did not have this coating.
The page linked above mentions that keyboards in these units have a high failure rate. I've also heard reports of G73x laptops with dead keyboards elsewhere.
The page linked above states that the power jacks are held on very weakly, and as such can crack off the board easily should someone trip over the cable.
Specifically for the G732 models - the CPU power fuse was slightly underpowered from the factory (2 amp), and could blow with the maximum supported CPU (3.06GHz HT) installed. If you have a completely dead G732 with this CPU installed, this fuse may have to be replaced with a higher rated one. I'd recommend avoiding installing a 3.06GHz CPU unless you're aware of the risks.
The page above states that the connection between the display cable and the motherboard may be flawed. DeltaDon had run into several that experienced failures characteristic of overheating there. It's unclear whether this was due to a design flaw or user error (spilling something on the computer, overheating).
I've seen someone with a Green736 laptop, which is a later higher-performance version of the Green732 (same casing) with stress cracks in the LCD housing around one of the hinge mounts. This may be an issue that can crop up, and may also grow more common as the plastics age.
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