My 2014 MCS has been jumping out of first gear sporadically the last few months. (Stick shift)Yesterday, I narrowly missed getting rear ended at a busy intersection because it happened again.Has anyone else experienced this problem?

 

This is a issue that has been discussed widely for the F56 unfortunately. I have seen somewhere where they said they have a shift collar repair kit available for vehicles having this issue. I'm assuming you're still under warranty so I'd suggest you call up your dealer and inform them of the issue and see what they have to say.

Cooper S jumping out of 1st gear!!!! - Page 3 - 2015 Mini Cooper Forum
First gear problem... - North American Motoring