Two problems related to water pump have 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.
Prematurely failing: struts (repaired summer of 2013), water pump (repaired 10/15/13), brakes (repaired 10/15/13), and alternator (yet to be repaired).
Two issues: radio controls fail; usually when outside temps near/above 100f. Touching any control turns off radio, spits out cd. Causes me to focus on radio instead of driving. Dealer no help. Seen the problem listed by others online inc. Youtube video of the radio acting up. 2nd issue: just had to replace water pump, approx. 150,000 miles. Appears there was some sort of recall but I did not receive any notice. Replaced 7/16/16.