I think it would be hard to maintain an intercontinental bridge. Think about the movement of the continents relative to each other. Then the bridge would need to be able to move asweel. We can't just plop down a billion concrete pillars into the ocean to hold the bridge.
The bridge will have to be built in a very smart way.
I have to disagree with you:
It's true that continents move, but they do it by a few centimeters per years. Our bridges can already "move" as they can expand and contract because of the heat with special joints (For example when you go in the highway on a bridge, you can hear some little regular "bumps" when the car passes over one of this joints). Moreover I higly doubt that any building of our time can survive more than a few centuries intact and usable. At last, even if a bridge is build in a very strong way that it can survive so long that the continents moved a considerable way (sorry for the long phrase
), we can always make the bridge shorter or longer adding or removing a little section of a few meters every, let's say, 100 years.