Three problems related to manifold/header/muffler/tail pipe have been reported for the 2013 Toyota Tundra. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2013 Toyota Tundra based on all problems reported for the 2013 Tundra.
Cam tower oil leaks on both driver and passenger side - oil leaking onto to manifold causing smoke - possible fire risk - numerous complaints went unanswered, finally diagnosed by the dealer, however Toyota not willing to fix as vehicle is outside of manufacturer's warranty - this is a known issue!!.
Cam tower gaskets (right and left) leaking @ 25,000 mi/5 years on exhaust manifold causing smoke and a fire hazard. Truck would not pass maine state inspection because of the oil leak.
Continuous oil leak from cam tower onto exhaust manifold. Dealer denied the issue even though the signs are very obvious. A call to Toyota to got me no where. They denied the issue like the dealer. There is oil on the engine block and also the exhaust manifold is black from the all of the oil dripping. After driving for awhile the car smells like it's burning. There is a very real potential for fire. The issue appears to be widespread. A quick internet search can find extensive examples. Toyota appears to be reverting to it's old ways and not taking responsibility for serious safety issues.