What are some of the BMW X1 differential problems?

If there is a humming noise coming from the BMW X1 then it can be caused by a couple of things. If the noise is consistent across all speeds then You likely have cupping in the tires. Cupping happens when the tires have uneven tread wear, making it so sections of the tire are higher than others. This will cause them to pick up and carry small bits of road debris and can lead to the humming sound. This is not dangerous, but it will make it so Your tires continue to wear, and You will need to get new ones at some point. If the humming increases in sound as You accelerate then You have loose wheel bearings in the differential. The bearings are moving in the sockets, and this is causing them to hum. You will need to have this looked at sooner rather than later. You may also get a knocking or front end sound, due to light lubrication.