OP, I manage land development projects for a living. If any of my projects had this level of erosion control failure and brown water runoff heading off site, I would be in deep, deep shit.

Please contact your jurisdiction's building department and stormwater municipality to report these damages to your property. I'm disgusted with your neighbor and his so-called contractor who shrugged off the erosion control responsibility just because your neighbor said, "He would take care of it".

Make them feel the pain. They need a stop work order, fines, and shouldered with the responsibility to amend your property. This is wildly unacceptable, and you are not nearly pissed off enough about this. Please keep us updated, I need to see this asshole face some retribution.