I feel that the best way to deal with any challenges is to meet them head on. When I found that one of my colleagues was saying things that weren't true behind my back, I went to him and talked it through. It turned out that he had misunderstood what I had said, and I was able to set the record straight with him, and my supervisor.
"Once I found a major flaw in the work of one of the most senior members of the department, which could have been very costly to the company if it had been overlooked. I went directly to him, and called it to his attention so he could fix it before it affected the final outcome