Perhaps Giggs isn't quite AS one footed, but regardless of Giggs' abilities with his right, he often chooses to go with his left to the detriment of the play. I think it's a matter of confidence. Giggs probably often feels more confident sending in a pass with the outside of his left foot than with his right foot. I'd wager it's largely confidence with Valencia, as well. The one play where he seemingly had a good shot from his left foot, but he hesitated, and lost the chance. That's a confidence issue first and foremost. Perhaps for a reason, but sometimes in that position you have to put it on the goal and see what happens. (Note, this is not to disparage Antonio in any way, I love the lad).
You'd think they have special drills for him. Juggling with his left foot, practicing cross after cross after cross and shot after shot after shot. But then again, I'd think he's been doing that for years and years to work on his left foot. With athletes that need both hands (basketball, for instance), they will often do everything around the house with their off hand. Eat with it, wipe their ass with it, wank with it, etc. All to build that coordination. Can't really do too much around the house with one foot, though.