How did Gates's errors in leadership contribute to the American loss at Camden?
Gates may have had a bit of bad luck.
Gates had amassed a fairly large force to attack the British. He had to march through a hostile area with many loyalist supporters. Many of his troops fell ill and many were not fit to fight.
The Battle was a meeting engagement so he could not view the enemies deployment and counter it.
Cornwallis was sharp and aggressive. He moved to engage Gates when he became aware of his presence. He attacked first when he saw the advantage.
Gates did not understand that his army was not quite fit to withstand a British attack in open ground at the time. His successor Greene understood this much better. Greene's dispositions at Guilford Court House with its 3 defensive lines and its objective of causing the maximum British casualties shows this. If Gates could have found a good defensive position, time to prepare it and the good fortune to get the British to attack it things may have worked out better. Gates' own experience at Yorktown would have shown this.
Gates disposition of putting his best troops on his right has been held a a mistake but armies have been putting their best troops on the right since ancient times and the meeting engagement type of battle makes last minute changing of formations difficult and unwise.
That his inexperienced and less well equipped troops on his left routed under the British attack was more of a problem. The British also put their best troops on their right.
Greene's strategy of eliminating pockets of Loyalist support, attacking supply lines and inflicting British casualties was more effective and eventually forced Cornwallis out of the Carolinas. This was more of a Guerrilla Strategy.