The OPDA (oil pump drive assembly) assembly was redesigned in 05 which caused a serious lubrication problem for itself. If it happens and it's not resolved right away it can take the cam out. There have been two aftermarket kits designed to help with that problem but neither proved to be a 100% permanent fix in all cases. Not to mention they're not always easy to get installed and working properly due to how installing it will screw up the engine timing if you don't get it right.
This forum has a thread on the OPDA issue at
https://wranglertjforum.com/threads/what-is-the-opda-and-do-i-need-to-change-mine.80/
The other problem is with the automatic transmission controller which has some serious software bugs in it. Fortunately there's finally a fix for that by replacing the PCM with one from
www.wranglerfix.com but it's still something that would likely eventually happen with the automatic your LJ most likely has. Hard shifts, shifting problems, transmission lockup, overheating codes, etc.. Not to mention the 05/06 PCM can cause other issues like with the O2 sensors.
There are some who claim there aren't any problems but they're either clueless or purposely misleading people who no nothing about the above issues and not equipping them to make informed and educated decisions.