What were the thinking when they built this wall??? The problem is water landing on the concrete and seeping back into your house under the bottom plate. Good construction allows the water to sheet off the wall, past the slab and to the ground. Gravity is your best friend in that case.
Caulking inside just seals the water inside your framing, causing mold and wood rot. Caulking outside is a temporary fix which will always fail over time.
You have to stop the water outside and allow the inside to dry out (eventually). That will take a rework of your exterior wall. Here is a construction diagram (do not let it panic you) of a typical stucco exterior wall. Notice the bottom left side has a weep channel which sheds the water away from the concrete (which is shown on the bottom right). You need to build an add-on which sheds the water similarly. I do not like the aesthetics of a false wall with matching siding and a drip edge ... but that might be your only practical solution. Perhaps adding a sloped concrete border at the bottom of the wall with proper bottom flashing above it would be nicer.
I would ask a few local contractors to offer on-site solutions. You do not have to take their ideas or spend the money. But, this is probably not the only building in the area where this fool did something similarly.
Last edited by CallMeVilla; 04-06-2013 at 09:20 AM.