Does Satoshi Dice owe its customers money? How come? From this analysis thread:

SD Profit after fees:       22476.66146080 BTC (1.688%)
Pending Liabilities:         6821.78965204 BTC
Final SD Profit:            15654.87180876 BTC


...


  From now on my reports will include this 'pending liabilities' figure
  since it's really getting out of hand.  There are bets going back 5
  days which haven't been paid out, almost all of them are winning bets.
  In total SDICE currently owes its customers around 6800 BTC, or around
  $91,000 US in unpaid bets.


How come there are unpaid bets going back 5 days? Does Satoshi Dice always pay immediately?
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".