As per Dave above, no common faults specific to the GS430. All the usual suspects for all of the older models. Calipers/slidepins is the main one, nothing else "common" springs to mind. The GS430 had the uprated brake accumulator right from the start, so not a problem with that uinlike the early GS300's.
Never driven or even been in an LS, so can't comment from a comparison perspective. The GS is smooth, quiet and very, very quick.