If your Nintendo Wii Remote has sticky buttons, see the Nintendo Wii Remote Buttons Stick problem page for possible problems and solutions.
Have you got access to another remote? This will prove whether the problem is with the remote or the console. If the remote is the problem, it may be that the contacts under the arrow buttons are either oxidized or worn by usage.
Here is a link that gives a general idea of how to repair a remote. I would recommend that if you need to pry open the case (because there aren't any screws) that you don't use a small screwdriver as shown in the video. It causes too much cosmetic damage. Use a broad-bladed tool such as a 1" paint scraper. It spreads the pressure over a wider area and causes less damage. If cleaning the contacts doesn't solve the problem because they are worn by being used a lot, you may be able to 'paint' just the contact area of the rubber button with silver conducting paint, which is usually available from electronics parts stores.