Aside from the brutality of creating the Mongol Empire the only real negative impact of its existence was the rapid spread of the Black Death in the 14th Century.
Other than the spread of disease, the empire connected the far east with India, Mesopotamia, Persia, Eastern Europe and the Levant under a single governing authority that facilitated trade and enforced a degree of religious freedom in traditionally Christian and Moslem strongholds. The total control of an east-west caravan route was the first time anything like that had ever been accomplished, though the Persian Kings Xerxes and Darius the Great came close to accomplishing it nearly 1,800 years earlier. Arguably all of the problems of the 21st Century can be traced back to the collapse of the Mongol Empire. Its collapse set off a chain reaction of events that led to everything that is happening in the world today.