Flaws that facilitated the Mongol Invasion
I believe that Andrew II of Hungary had by mistake opened two wholes in the Eastern natural defence of Transylvania that invited in the Mongols for an easy attack of plunder. It is possible that historiography today contain a mystification of the events past. I am highlighting the very bizarre narratives pertaining to the events at Peter Clings's answer to How could the Mongol invaders defeat the Hungarian Kingdom in one battle only in 1241?
In an effort to expand more his realm to the east, the King had invited in the Teutonic Knights at Burzenland with the intention to dominated the lower Moldavian plains via that proxy. The order operated in the region, between 1211 to 1225 eliminating all regional competition in that Carpathian crossing. In a foolish attempt to consolidate trade with the Cumans who dominated the Moldavian plains those times, they established also a Catholic Bishopric and endowed it with gifts that made the headlines on the Eurasian steppe again. But, the Teutonic Knights being expelled, that left a major gap of defence through which one of the column of Mongol attack penetrated Transylvania from south devastating all the cities in its path. The Cuman Bishopric was more like placing a big and visible sign pole indicating the entry point in Transylvania (a very strange weakness)
A second effort of expansion to the North East was to take over the Principality of Halych
For the conquest of the new principality, they opened a new corridor called Tihuța Pass
, which was too recent to have built yet any local defence. Through it, a second Mongol invading column penetrated Transylvania from North East, devastating all its Northern cities. That invading force was led by a Mongol general called Koten (more on that First Mongol Invasion through Transylvania)
To the south, Bela IV was conducting a bloody crusades against some unspecified heretics in Bosnia from 1235 to 1241 (see Bosnian Crusade). Rumours of serious misconducts during that war of conquest must had propagated within his newly arrived guest Cumans who were pagans themselves. At the Battle of Mohi, the entire army of the King consisted of his contingents coming back from the Bosnian Crusade, including a contingent of Templar Knights from upper Slavonia (see map at Peter Clings's answer to Why did the Knights Templars not receive any grants in Transylvania? ). The Cumans lost trust of the hosting King and moved south pillaging and destroying the country alongside the Mongols
But historiography may be mystifying events. As the narrative presents itself a few very weird inconsistencies transpire. See more at How could the Mongol invaders defeat the Hungarian Kingdom in one battle only in 1241?