Anyone can play softy, but of course it takes time and alot of good listening to master the correct touch and tone you strive for. For starters, it helps to play p passages very slowly, one hand at a time and listen carefully to the sound you are producing. Keep your fingers and wrists loose. If you press a key down lightly you will feel a bump before its depressed completely. My teacher advises me to play "before the bump" so you should imagine playing so lightly that the key sounds but never actaully "hits" the bump. This, of course, is not to say that you shouldn't press the key down all the way; it more visual than literal, but is good advice, especially with fast repeated notes in pp. As others have said, it also helps to keep your fingers very close and connected to the keys, which will work equally well for soft stacatto or legato passages. Some have a tendency to lift their fingers high to achieve accuracy and eveness, but so many teachers have told me that this approach actually diminishes the quality of sound and produces tension in the hand. However, I've found that objectively listening to yourself is often better than simply applying specific technical adivice. Good ears can be trainied to pick up a wrong pp sound, for instance, but only with a lot of experimenting and patience...and a great Steinway never hurts!
If you use the una corda to "hide" the problem areas, it really won't help you out at all. If you are playing p passages incorrectly from the start and put on the u c, yes it will make your playing sound superficially softer, but the piano will be doing the work, not you. You should only consider using this pedal for tonal effect, not as a technical tool. Once you achieve the pianissimo sound and touch you want (and you will) then if you wish, you can use the u c for a change of sonority.