Learn Danish: Han tror nok, huset er ved at forfalde. - He probably thinks the house is decaying.

The structure være ved at + infinitive emphasizes an ongoing process or transition. While huset forfalder could just state the general fact that the house is in a state of decay, using er ved at forfalde specifically highlights that the deterioration is an active, continuous process happening right now.

Is there a word missing after the comma?

Yes, the conjunction at (that) has been left out, which is extremely common in everyday Danish, just like in English. The full clause would be at huset er ved at forfalde. The comma remains to mark the boundary between the main clause and the subordinate clause.

What nuance does the word nok add to tror in this sentence?

Nok is a modal particle meaning "probably" or "likely." Adding it to tror (thinks/believes) softens the statement, indicating that the speaker is making a strong assumption about what the man thinks, but isn't entirely certain.

Does the verb forfalde apply to anything that decays, such as an apple?

No, forfalde is primarily used for buildings, structures, or institutions that are falling into ruin, disrepair, or decline. If you want to talk about organic matter like food decaying or rotting, you would use the verb rådne.