A statement can be clear, accurate, precise, relevant and deep — and still be flawed. What two standards catch that case?

Breadth (is it one-sided?) and logic (does the conclusion actually follow?).

Even a statement that passes the whole earlier stack can fail two further tests:

• Breadth / differentiation (Vernetzung): it may be one-sided — true and deep but blind to other enriching standpoints. The probe: "Is there another perspective on this problem?" Considering only your own angle, however well, leaves the picture partial.
• Logic (Logik): does the conclusion actually follow from the premises, or is there a fallacy? Are the assumptions even true? Were the criteria of argument respected? This is where a chain of individually fine statements can still add up to an invalid argument.

Tip: Breadth guards against the well-argued echo chamber; logic guards against valid-looking-but-broken inference. Both can fail after a claim is clear, true, precise, relevant and deep.