As for swapping LCDs, its a lot more possible with the TE than with other systems, but I'm not sure I've ever seen it done.
As for "other problems" with other versions of the PC Engine, they are fairly well documented. The number one issue is with CDROMs. For the Duo line the CDROM lens can still be found online, and many people here have replaced them. The other major issue is with sound in the Express/GT, and original black Duos. This is almost always the fault of failing capacitors, and many people here have replaced those as well.
There is also a problem with original CDROM units stripping out their gears, and of course there is the region hack that needs to be done to fully enjoy these systems. Getting better composite and also s-video is also possible with after market chips.
I think that pretty much covers it since NEC systems are fairly reliable. Much of the info on those subjects can be found here in these forums.