Learn Russian: Вам нужно ликвидировать ошибку.

Context is our only clue here. Because the goal is to achieve a single, completed result—fixing a specific error—ликвидировать is acting as a perfective verb. If the sentence contained a habitual trigger like часто (often), it would act as an imperfective verb instead.

Could ликвидировать be interpreted as imperfective here, even without extra words?

Technically yes, but it would make less sense. As an imperfective, it would mean you need to be in the process of eliminating the error, or that you need to regularly eliminate it. Because a single error (ошибку) is usually fixed just once, the perfective interpretation is the most natural.

The word ликвидировать looks like the English word liquidate. Is it too dramatic to use for an error?

Not in Russian. While it can mean liquidate in a dramatic sense, it is also a standard, formal verb for eliminating something negative. Collocations like ликвидировать ошибку (eliminate an error) or ликвидировать проблему (resolve a problem) are completely normal in professional contexts.

Just to review, why do we use the dative Вам here instead of the nominative Вы?

This relies on an impersonal construction. The word нужно (it is necessary) doesn't describe an action that a subject is actively doing; rather, it describes a state of need that applies to someone. In Russian, the person experiencing that need takes the dative case.