Anyone old enough to remember huge CRT televisions, will remember a surefire repair: hit them. Apparently, the Wii Remote works in much a similar way.
On Nintendo's official Japanese FAQ site, one question asks what one should do if their Wii Remote buttons or motion sensing doesn't work. "In that situation, it's possible to rectify the issue by hitting the Wii Remote against your open palm."
Nintendo has an illustration that shows how: It seems "lightly" hitting near the Dpad is optimal, and be sure to take off those Wii Remote sleeves.