Learn Swedish: Det gäller att inspektera den där målningen noga. - It is crucial to inspect that painting closely.

The verb gäller on its own usually means "applies" or "is valid," but the impersonal phrase det gäller att is a common idiom meaning "it is important to," "it is necessary to," or "it's all about." It is followed directly by an infinitive verb (here, inspektera) to express that an action is a crucial requirement.

Could I just say man måste inspektera instead of det gäller att inspektera?

Yes, man måste (one must) conveys a very similar meaning. However, det gäller att shifts the focus away from the person doing the action and entirely onto the action itself. It adds a tone of high importance or presents a critical condition for success, similar to saying "the key is to inspect" in English.

Why does målningen have the definite -en ending if we already have den där (that) before it?

This is the Swedish double definiteness rule at work. Whenever you use the demonstrative phrases den här (this) or den där (that), the noun that follows must also be in its definite form. That is why we use målningen (the painting) instead of just the indefinite målning.

Can I use noggrant instead of noga as the adverb for "closely" here?