One problem related to clutch broken has been reported for the 2013 Nissan 370Z. The most recently reported issues are listed below.
***Nissan 2013 370z (mt) clutch slave cylinder *** purchase brand new. In March of 2013, just 2k miles the slave cylinder failed. Replaced under warranty. On 6/17/2016, I was driving on the freeway, my clutch failed during traffic hours on the 60 east fwy. I could not shift the gear to get to lower or higher gear. Thank god I was able to get on the shoulder lane to stop safely. This happened at 3,100 miles. Yes, just after my factory warranty had just expired. Csc is not covered under powertrain warranty but Nissan has agreed to fully pay for the second replacement. This is clearly a safety issue and can cause bodily harm when driving and clutch fails. Also I belong to a Nissan social community forums and there are many have had the same issue. This should be a recall. Be safe out there.