Priority inversion
A high-priority task ends up effectively waiting on a low-priority one, because a medium-priority task is in the way.
It takes three tasks. Low holds a mutex. High wants the same mutex and blocks. Medium, which doesn't care about the mutex at all, becomes ready and preempts Low — so Low never gets to release the lock. High is now waiting on Medium, even though the scheduler is doing exactly what it was told.
The famous case happened on Mars in 1997, when the Pathfinder lander kept getting reset by its watchdog. JPL reproduced the bug on a replica on Earth and turned on priority inheritance in VxWorks by uplink: whoever holds the lock temporarily inherits the highest priority of anyone waiting for it. Sha, Rajkumar and Lehoczky had published the fix in 1990. The alternative, priority ceiling, is used in Ada and AUTOSAR among others.