More weight aloft. The additional weight of the battens pockets and extra hardware aloft makes the boat more tender in a breeze. It also makes the sail heavier to hoist. The lazyjacks tend to chafe the sail especially at the battens, as do the shrouds when sailing off the wind. This means frequent restitching and patching at the trouble spots.
Full battens have a strong tendency to hang up when the sail is being raised and lowered.
This problem can be largely eliminated with the right luff hardware at the batten ends, but the cost of this hardware ranges from high to astronomical. Batten tension must be adjusted to meet the conditions otherwise you may wind up with worse sail shapes than you would have with a conventional sail. This tensioning can be done in two different ways. Tensioning the battens in this way requires exerting quite a bit of force on the leech line, so it is advisable to run the line to the end of the boom and then forward toward the gooseneck where it is more accessible. Ideally, both methods are used by setting the basic tension with the pocket adjusters for the overall conditions you expect for the day and then fine tuning for varying conditions and point of sail with the leech-line to maintain optimal shape.