This is going to be dependent on a few factors.
Is there bacterial activity inside the zombie? Most corpses start decaying internally as gut bacteria spread out, causing bloat and putrefaction of internal organs. You could expect significant decay in 4-5 days in a fairly warm temperature. In hot environments it can happen in just a day or 2. But if the zombie creation process sterilizes the gut, then decay will occur much more slowly.
What is the ambient temp? Dehydration (and eventual mummification) in warmer, dryer areas is the ultimate fate of any zombie not consumed by gut bacteria. I would expect significant dehydration after just a few days in a dry, warm environment.
Mold and fungi from the skin and environment will start to grow on the dry and cracked areas of a zombie within a week or so. Moist areas exposed by cracked skin will be affected first.
Scavenger activity by ants and the like will be slow but eventual. If gut bacteria is dead, would fly larvae survive? They can set up in just a few days. A moving zombie will probably ward off most birds until they learn that the zombie is still good meat. Same with scavenger mammals like coyotes or hogs.
Assuming wholesale death of most humans into edible meat or edible zombies, there would be a lag in the explosive growth of scavenger animals and insects. Fly swarms, ants, and roaches would be the first. Scavenger birds, turkey vultures, and small mammals next. Larger mammals last, as well as animals that prey on the insect and small mammal swarms.
Lots of rotting meat can contaminate running water with gut bacteria that is harmful for humans to ingest, like e-coli. Fly populations can carry around harmful bacteria as well, as can rats. So urban areas with lots of dead bodies would be hazardous without protective gear (check out natural disaster recovery like from landslides or earthquakes to see what hazards there are).
Of course without humans around, there would be a concomitant die-off of human supported animal/plant systems. Lots of dead pets inside houses and dead cows, hogs and chickens in pens without food/water. Loose dogs would form packs and go feral, loose pigs would do the same. Loose cats would be fine, they are feral already :P