I can't garantee that ammonia leakage won't be a problem, but I would claim that we can't quantify the issue until we have good data from larger field trials.
However, I would expect that the ammonia leakage into water bodies from widespread transportation use would be very small compared to that produced by agriculture: ammonia is a gas at normal temperatures and pressures and evaporates rapidly if spilled, converting to a lighter-than-air gas which does not accumulate near the ground like gasoline fumes. In contrast, in agriculture, ammonia is injected directly into the ground, where it can disolve in moisture and be trapped there where it can be mobilized by rain. It's worth pointing out that ammonia is sometimes transported by ship over seas and by barge on rivers.
No doubt that DME is a more user-friendly fuel, which is especially important for in-door applications such as cooking. When made from sustainable energy sources (e.g. solar, wind, OTEC, or nuclear), it will be much less efficient and more more expensive per unit energy than ammonia, if the required carbon is obtained sustainably. Currently, CO2 capture from the air is not cost effective, and requires an amount of land almost on the same order of magnitude of as biofuel. Using CO2 captured from fossil fuel combustion (i.e. diverted from the sequestration path) is not sustainable or carbon neutral.
Starting from natural gas, DME is not made directly, but with methanol as an intermediate. Methanol and ammonia have about the same conversion efficiency (from natural gas), then the methanol to DME step adds additional efficiency loss and capital cost.
So even though DME is a great fuel, I don't see the benefits outweighing the cost compared to ammonia in automotive applications (same for trucks, trains, and cargo ships; as well as industrial process heat).