Are cans dishwasher safe
Washing cans in your dishwasher is not a good idea because of the labels. Most cans have paper labels which are held on by glue, in the dishwasher the labels will soften and come off, getting sucked into the mechanism and getting stuck to dishes and glasses. The dry cycle will harden the paper in place and be very hard to get off. The glue will also probably melt with a similar result. 

Cat food cans do tend to get a bit stinky, but a quick sink cleanup usually does the trick. Soak them in water for 10 minutes or so and then use a bottle brush with a drop of dish soap to clean them.