1. The Roman army arguably committed mass genocide multiple times. Gaul famously might've had its population cut by as much as 2/3, though most modern estimates are lower or still might've been 1,000,000 killed. Certainly over the centuries they were responsible for the deaths of potentially tens of millions.
2. They weren't "allowed" into the city of Rome, and this was for good reasons, but ultimately they proved willing to betray Rome in favor of any generals cult personality and/or promises of wealth. This resulted in not only two civil wars, but also turned the republic into a monarchy (The Roman Empire), led to the assassination of various emperors and generally an unstable government.
3. Much of ancient unwritten cultures was lost indefinitely. While Roman culture spread through conquest most conquered peoples were more or less forced to adopt ideas like Christianity, which you could argue isn't the Roman army's fault but effectively is a direct result of their victories. Most of what we know about the Celts for example was just written by Julius Ceaser who really seemed to despise most of them. Later historians and Christian scribes would paint every conquest as entirely justified and in a way "whitewash" everybody's history. Thats just a terrible shame, I wish at least some of the oral traditions were past on, but oh well.