The problem is much like the author said -- it's easy to have errors disappear into the ether in a way that is much less likely in synchronous logic. Also, if those side-effects matter, it's easy to make faulty assumptions about time ordering.
The most obvious situation to me is in the way asynchrony exists in front-end programming and how this affects testability. If you can't actually know when a process (like an animation) ends, you can't accurately test.
In general, my experience has been that reification of abstract things often presents benefits in the long run. Reification of functions admits a whole host of techniques. Reification of classes facilitates metaprogramming. Reification of in-flight processes as promises helps with being able to compose and abstract over them. Nurseries seem like reficiation of an finite execution context.