It appears that some iPad Smart Covers aren't working properly with the new iPad, including older Apple Smart Covers. The new iPad has a slight change in how its magnets work. Apple has reversed the polarity of one set of magnets related to the sleep/wake sensor that turns the iPad off when the Smart Cover is closed. As a result, older Smart Covers, that weren't designed with this change in mind, fail to turn the new iPad off when they're closed.
Mark Booth has more details as to why Apple choose to make the change:
I've learned why Apple decided to use a polarity sensitive switch in the new iPad 3. Some iPad 2 customers were having issues with their iPads entering sleep mode when they flipped Apple's Smart Cover around flat behind their iPad 2. Since the iPad 2's sleep/wake sensor wasn't polarity specific, it could sometimes be triggered from the magnet being positioned at the rear of the iPad. By changing to a sensor that requires the correct polarity, the problem is eliminated.
Booth also notes that Apple is replacing older Apple Smart Covers at Apple Stores for customers who ask. New iPad owners having difficulties with third-party smart cover-compatible cases should contact their case-makers for possible resolutions.