Here are the controversies he has done (from Wikipedia):

At UFC 48, held on June 19, 2004, Herb Dean refereed a bout between Tim Sylvia and Frank Mir for the vacant UFC Heavyweight Championship belt. At :50 of round one, the fight was called to a stop after Herb Dean saw a break in Sylvia's right forearm from an armbar by Mir. Sylvia claimed there was nothing wrong with his arm and wanted the fight resumed, but it was later found Sylvia had suffered multiple fractures.

At UFC 61, held on July 8th, 2006, Herb Dean served as referee of the highly anticipated rematch between Tito Ortiz and Ken Shamrock. At 1:18 into the first round, Dean stepped in and stopped the fight following several consecutive elbows to the head of Shamrock by Ortiz, giving the victory to Ortiz by TKO. Shamrock, visibly angered, immediately protested the decision. However, it was not overturned and Shamrock was subsequently ushered out of the Octagon. A rematch was held during Ortiz vs. Shamrock 3: The Final Chapter with Ortiz once again claiming victory in a very similar fashion to the second fight, although Shamrock did not question this decision. [1]

At UFC 66, held on December 30, 2006, Herb Dean refereed a fight between Andrei Arlovski and Marcio Cruz. Arlovski landed an illegal head kick on the ground to Cruz, causing Dean to pause the fight momentarily. He began to stand the fighters up and warn Arlovski, but Cruz complained about wanting to keep the fight on the ground. Dean agreed to restart the fight in the same position, and once he let the fighters start Arlovski landed the big KO. Not as controversial as the others mentioned, but due to the position on the ground (attempted leglock) the fight needed to be stood up at that point.