Learn Dutch: Waarom wordt de muur zo smerig? - Why is the wall becoming so filthy?

English frequently uses the continuous tense ("is becoming") for things happening right now, but Dutch typically just uses the simple present tense. So, the single word wordt translates to both "becomes" and "is becoming" depending on what sounds most natural in English.

worden is also used to form the passive voice. How do I know it means "becoming" in this sentence?

You can tell by looking at the other words in the sentence. When worden is paired with an adjective (like smerig) or a noun, it acts as a linking verb meaning "to become". If it were paired with a past participle (like geschilderd - painted), it would form the passive voice, as in De muur wordt geschilderd (The wall is being painted).

How would I say "Why has the wall become so filthy?" using the perfect tense?

To form the perfect tense of worden, you must use zijn (to be) as the helping verb rather than hebben, along with the past participle geworden. The sentence would be: Waarom is de muur zo smerig geworden?

I usually use vies for "dirty". Is smerig different?

They are very similar, but smerig is a stronger word. While vies just means "dirty", smerig translates closer to "filthy", "grimy", or "foul".