Poor King Mark. All he wanted to do was marry a nice girl and live happily ever after. Or, at least, that's what his knights told him he should do, and he went along with it. How could he have guessed that a magical mix-up would put him in the middle of a love triangle, forever complicating his dreams of wedded bliss? Just like it's not really Tristan and Yseut's fault that they fall in love, it's not Mark's fault that he happens to be the guy who marries Yseut. That doesn't stop other characters from accusing Mark of being too quick to believe the "lies" of his barons. Even Arthur, a fellow king who you'd think might be sympathetic to Mark's situation, accuses him of being "easily influenced" by "false words" (15.140).
Is there any truth to these charges of excessive gullibility on Mark's part? Well, it is true that Tristan has been nothing but loyal to him in the past. And it's not clear at first why Mark chooses to believe the word of his barons over the word of his wife and nephew, before he has any evidence of wrongdoing.
Of course, Mark's barons turn out to be right. The problem with Mark's character is not that he believes that Tristan and Yseut are having an affair: it's that he just can't seem to commit one way or the other. As Perinis explains to Arthur, "the King's mind is not steadfast: sometimes he thinks one thing, sometimes another" (14.124). Mark could save himself a lot of trouble if he could just trust his own judgment from the start. Mark's inability to commit to a course of action is understandable, but it's not a good trait for a King whose vassals depend upon his decision-making ability.
Other evidence of Mark's weakness as a King includes his loss of Yseut to a clever harper and his refusal to give Tristan and Yseut a fair trial when his anger at them trumps his people's repeated requests that he do so. In everything he does, Mark is guided by emotion rather than reason, a trait that makes him a sympathetic character but a bad king.