The most common seems to be:
Front lower control arm bushings go bad early. Bushings are not that expensive, but the labor can add up.
Front differential bearings on early years. Seems to be related to a coating that LR appied to the inside of the case flaking off. Some say that most trucks have been through this already and the problem is slowly going away.
Sunroof drain leaks and wet floorboards from them.
Rear lower tailgate release mechanism fails.
Transmission computer can get wet and corrode the terminals if not cared for after a river fording or engine wash. Some say this can also happen if you use a non-correct battery and don't reconnect the battery vent.
Various ECUs randomly spitting codes. This is the result of a low/failing battery or alternator. The concensus is that a LR3 needs a new battery every 3 years regardless of the warrenty on them.
Air compressor. Some say the main reason they fail is because the dryer/disecant never gets replaced so it plugs making the compressor work harder to push air and eventually fail.
Other than that, alot of the 'bad rep' is the trouble in reading and clearing codes/errors. Invest in an appropriate tool (Faultmate/IIDtool) to clear codes yourself, and I'm sure the overall experiance will be no worse than any other truck.