Actually a sloped run and a slope leading to the coop may be an advantage, depending in how steep the slope is. You know where the water is coming from. You can fix your drainage to keep the water out of both coop and run. I prefer a berm built up to direct the water instead of digging a ditch, and you have to be a bit careful about concentrating the water and causing severe erosion, but I used terrain to help keep my coop and run dry.
I don't know of any disadvantages of having it close to the vegetable garden as long as you are not blocking sunshine or creating an erosion problem. The chicken poop really needs to be composted before it goes on the garden, so consider how run-off would work. One advantage to having the run close is that I often feed mine stuff from the garden, excess green stuff like cabbage leaves or kale or chard leaves that bugs got to, bad tomatoes, squash, or peppers, corn ear worms, various things.
Depending on how steep it is, the run really does not need to be level. What you want to avoid, other than drainage and erosion problems (watch how you slope your coop roof for rain runoff) is that they may be easily able to fly out over the lower section. You may have to build up your fence down there to keep them in. I really can't think of any other potential problems.