Most of earth's usable land would now be used for legume crops to make up for the loss of protein from animals. They would use chemical fertilizers. More chemicals in the watersheds equals more pollution. Land used for pasture would be turned into soybeans as well as many forested areas. Clear-cutting would destroy much of the earth's remaining forests, causing hundreds if not thousands of species to go extinct. There would be less crop rotation as there would be less demand for rotation crops such as feed corn. The soil quality would go WAY down. The nutritious value of our foods would suffer as a result and the prices would soar. GMO's would be absolutely necessary to sustain the population and large farm operations would likely dominate the global economy. Demand for food variety would increase due to the phasing out of unethical varieties and practices. Sugar comes to mind. Vegans don't eat the majority of white sugars because it is filtered through bone char. So limited exotic imports like blue agave and raw cane sugar would be expensive. Sweets would be rare and pricy. There would be an increase in cotton and bamboo manufacture (with the necessary space and chemicals) and synthetic fabrics as well to fill the gap of wool and leather. Oil production would therefore go up to meet the demand of synthetics of all kinds.
*Widespread famine would occur in desert regions that cannot grow crops or keep domesticated animals. No camels or goats (the most eaten meat in the world) for food would spell disaster for much of the arid world. Bumper crops and crop failures would likely cause international discourse, possibly war.
*Healthcare would suffer as no lab testing on rats or mice would be permitted so drugs would have to be tested on the population or in theory. But by this time, there would probably not be much of a population to save.
In theory, all of the domesticated animals as we know them would eventually go extinct. There may be some stray populations that are wild and dangerous, such as packs of feral dogs and pigs but the authorities would be on it, capturing them and sending them to the remaining sanctuaries to live out their days in relative confinement.
Except those who opposed the vegan regime. They would secretly keep small herds of cattle and pigs and sell them on the black market... like in the Hunger Games.
I'm sure there's a lot more global impacts but that's what I imagine would happen.