Upon an initial check of the data of Pokémon from the Trainer House compared to the actual data that is and isn't transferred to the Pokewalker is as follows.
Data that is transferred to the Pokewalker includes: PID, EXP (but if it has the Pokémon be above Lv 50 the Pokémon is rounded down to Lv 50), nature item, ability, friendship, IVs, EVs, attacks, TID, SID, and trainer gender.
Data not transferred over to the Pokewalker includes: origin game, met location, Poke Ball, met level, met date, fateful encounter flag, encountered on, egg met conditions, OT, and ribbons.
Data not checked includes: language, Pkrus flags, shiny leaf flags, nickname (but if my memory is right that data is transferred), contest stats, and extra bytes.