In fact, "trying all possibilities at the same time" is a ubiquitous phenomenon in Nature. Light rays find their trajectory by tryin out all possible paths and only the one with the highest constructive interference survives (this is what Feynman discovered in Quantum Electrodynamics, which is referenced in the article).
The real trick in quantum computing is manipulating qubits through quantum gates such that the outcome that gets assigned the highest probability is the correct one. This is indeed hard as the environment usually interferes and spreads out the probabilities across all outcomes, leading to a junky, random outcome.
"In order to maintain a quantum superposition, we have to follow very strict rules imposed by quantum mechanics. We can't make operations depend on the state, so nothing like an if statement is available. Also all operations have to be reversible, so we don't have logical 'and' or 'or'. A relative handful of programs can follow these rules and get a huge speedup from quantum parallelism. The vast majority of useful computer programs can't be rewritten this way and get little or no speedup."
From the article: The goal in devising an algorithm for a quantum computer is to choreograph a pattern of constructive and destructive interference so that for each wrong answer the contributions to its amplitude cancel each other out, whereas for the right answer the contributions reinforce each other.