One problem related to manifold/header/muffler/tail pipe has been reported for the 2012 Hyundai Veloster. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2012 Hyundai Veloster based on all problems reported for the 2012 Veloster.
My car has code of p0420 catalyst system efficiency below threshold. The mechanic I have had look into the cause has suggested replacing the exhaust manifold catalytic converter assembly due to catalytic converter failure. It's a 2012 Hyundai Veloster 1. 6 liter non-turbo, the same engine that is included in one of the largest recalls on your site. My vehicle though is not included and I feel it probably should be due to having catalytic converter failure, likely due to design flaw if others are having similar failures.