Back when I used to do hydroseeding and erosion control, I used to run into a lot of ugly ditch situations. Seems everytime some developer would start a new development, they had to fight water run off in one direction or the other. Bare ditches just washed deeper and deeper. Fill the ditch full of riprap and then it would clog up with leaves and other junk that would find its way down the ditch. The best method I found to fix the problem was to slope the ditches where you could run a regular mower up and down the sides. After slopeing, seed the area and apply Turf re-enforcement mats. (TRM's) The grass would grow up thru the mats and the mats prevented the water from washing the ditch out. Because the TRM's made for a smooth surface, the ditches where pretty much self cleaning and any leaves or trash would just flow on down. You might talk to you neighbor and see if they will go along with doing some minor grade work. All it would take is a tractor and scrape to smooth the side of the ditch. I used to use my harley rake and just run down each side letting the rake smooth and level the sides and once done, it was just a matter of spreading seed and rolling out the mat. The mat needs to be stapled to the ground to prevent it from washing out, but once the grass is established, the grass will hold it in place. TRMs really makes maintaining ditch banks as simple as making a pass with the lawn mower.