The black flex pipe entering the top of the disposal is the dishwasher drainpipe, and it is secured at a high point.
The little valve on the lower left is the dishwasher hookup. Notice the short upright copper tube? That is a water hammer arrestor, be glad you have one. Only issue I see is that the vent for the drainpipe is too low, needs to be as high as possible. If you haven't had any leaks, no biggie.
We ditched the sink disposal, as I have a 42 year old house with cast iron drainpipes under the slab, and got tired of clogs & disposals seizing. Haven't looked back since.
Funny thing is, my neighbor came over and said that she has water running down her window every time she turns the disposer on. I went over and said "show me", then I pissed my pants laughing so hard. Her drainpipe was so clogged, every time she ran the disposal, it was forcing all the water up and out of the vent pipe on the roof, making it run down her window....
