Question regarding PSP and applying to companies

Last year in December before I had my CDL I was pulled over by CHP while pulling a trailer for the school district I work for, for driving in the wrong lane while pulling a trailer. While pulled over he also gave me a level 2 inspection which included 5 vehicle violations. They were no carrier/DOT number on the truck, inop brake and turn signals, and license plate was mounted vertically. I was not cited on any of them, but I know all 6 violations on the inspection show up on my PSP. Do I need to list the vehicle violations when I apply, or just the one moving violation which was being in the wrong lane? And will those violations hurt me when trying to get a job? Other than that 1 inspection I have nothing else on my MVR or PSP.

 

I paid the $10 to see my PSP and it is definitely on there. I'm worried companies will see the 1 moving violation and 5 vehicle violations and not want to give me the time of day. Which sucks considering that was the only time I've been pulled over in 14 years of driving vehicles.

 

The odd thing is me and my employer both didn't know it was a commercial vehicle. I'm employed by a school district and the vehicle was Chevy 3500 pulling a 20' utility trailer. It doesn't require any special license to drive.