Does Satoshi Dice owe its customers money? How come?
SatoshiDice pays most bets instantly, but for whatever reason sometimes bets get 'stuck'.

The issue you're referring to in your question happened during an exceptionally high volume period for SatoshiDice.  They received over 70,000 BTC worth of bets in a 24 hour period, which is much higher than usual.  The high turnover apparently causes issues with paying out in a timely fashion.  This was compounded by a bug which caused too much of SatoshiDice's BTC holdings to be transferred into cold storage.

As of this morning there is only one bet that hasn't been paid out.  It was a bet for 0.35 BTC, and it lost.  So to answer your question "No, they don't currently owe their customers money.  But sometimes they do fall behind for a few days".