How can I tell whether dictation actually saves me time?
Time the whole task, corrections included, before you decide dictation saves you anything. The summit notes include an enthusiastic case for replacing much of the keyboard with it, and the productivity numbers there are a speaker's claims, so test it on your own work.
Pick a task you do often, like a project update, and write down what the finished version has to include: current status, the decision needed, the person responsible and the date that matters.
Type one update and speak a comparable one, and hold both to the same standard for a usable result. Count the time spent fixing names, finding missing details and making the final version readable. A fast first draft that takes longer to repair hasn't necessarily saved anything.
Dictation may fit only part of the job
After several attempts, look for the task where speaking helps most. You might explain context clearly out loud and still prefer to type a table or edit exact language. You don't have to pick one input method for everything.
Match the setting and the tool to the information you're handling. A crowded room is no place to dictate confidential client details. Keep the experiment small enough to change.