I have been researching for the past day in two textbooks about the Yuan Dynasty for an essay in my Mandarin class and I've noticed something odd, but not surprising. (Of course, my research could have been too shallow) Khubilai did not seem to bring anything to the table in terms of advancement in any field (agriculture, government, culture, warfare, medicine) for the Yuan Dynasty. I am not too surprised by this because as a foreign invader, the Mongols probably wanted to control China for it's land, not to make some sort of advancement.
EDIT TO THE QUESTION: Long-term improvements
The most obvious benefit was political unification. Prior to the Yuan dynasty, China was split into two rival powers, the Jurchen-led Jin dynasty in the North and the Southern Song Dynasty. By conquering both states, the Mongols brought an end to the wars Song and Jin fought on and off over the 12th and 13th centuries. Of course, whether this was actually beneficial long term is debatable, since this also brought an end to the rapid improvements in gunpowder technology of this period.
On a larger scale, the Yuan dynasty's link to the other parts of the Mongol empire created a pax mongolica which facilitated trade and cultural exchange across the Asian continent. The most important exchange was with the Persians living under the Ilkhanate, who introduced various advances in the natural sciences and western crops.
So, in conclusion, the Mongols might not have directly introduced any advancements, but their unification of China and alliance with the Ilkhanate in Persia certainly created the conditions for advancements to occur.