One problem related to driveshaft has been reported for the 2010 Toyota Corolla. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2010 Toyota Corolla based on all problems reported for the 2010 Corolla.
Right side cv joint boot cracked, leaking grease @ 56k miles, discovered during routine inspection & could result in failure of cv joint disconnecting from hub assembly & loss of propulsion. (warranty expired) condition rectified by replacement of right side drive shaft assembly. This item should last far longer (I had a 1995 Corolla 14 yrs & 172k miles with original cv boots intact.