Issues with check-parse-results

So, we just merged https://github.com/microsoft/DefinitelyTyped-tools/pull/484, and there are some issues with it:

• The checks made by check-parse-results should ideally also run overnight to make sure everything is in order on DT, not only when there are PRs to this tools repo.
• check-parse-results seems to write from the logger, but the checks it performs don't write to the log, they throw instead (https://github.com/microsoft/DefinitelyTyped-tools/blob/master/packages/dtslint-runner/src/check-parse-results.ts#L34-L36). We should change the checks so they log instead of throwing. This would mean that we log all failures at once (instead of stopping on the first failure).
• The result of logging should show up somewhere visible. That's related to the first item above.

cc @jablko

Start with packages/dtslint-runner/src/check-parse-results.ts, especially the checks at lines 34–36, to understand the current throwing and logging behavior. Identify how these checks could run overnight and where their output would be visible. Done means overnight execution is covered, all failures are logged instead of stopping at the first, and the results appear somewhere visible.