The computer was working acceptably well. What it was doing was alarming out a condition where it was dropping some tasks (rendezvous radar angle processing) due to a switch misconfiguration.
The other parts of the code were running fine and caused no issues aside from the distraction of the alarms. Note also that he didn't nearly run out of fuel, although he did run relatively close to the mandatory abort limit. There was plenty of fuel to land, if they had ignored the abort limit. They landed with quite a bit of time at hover thrust levels.