I mostly manage my listing on my phone as I can do it on the go, in between taking care of my son, cooking, doing laundry, while I am at work, and relaxing on the couch.
The only issue I had was trying to access monthly discounts from my phone and airbnb support kept telling me how to get there and it was not correct. I had to log on to my computer to find what they were referencing. I understand there are different programs for mobile and computer interfaces but I should be able to find the same info under the same tabs (maybe in a different format) but it should be accessible on mobile and on the computer.