Learn Russian: Этот скандал вредит компании.

The verb вредит (from вредить, meaning to harm) is a verb of hindrance. In Russian, verbs that express helping, hindering, or harming take the Dative case without a preposition. You can think of the literal meaning as causing harm to the company.

Компании ends in -ии. Doesn't the Dative case usually end in -е for feminine nouns?

Most feminine nouns do take -е in the Dative case, but nouns ending in -ия (like компания) are an exception. For these nouns, the Dative, Prepositional, and Genitive cases all end in -ии.

Is вредит an imperfective or perfective verb here?

It is the imperfective verb вредить, conjugated in the present tense. It is used here because the scandal is currently and continuously harming the company. The perfective pair, which you would use for a completed action, is навредить.

Are there other common verbs of hindrance that work just like вредить?

Yes! Another very common one is мешать (to hinder / to disturb / to bother). Just like вредить, it requires the target to be in the Dative case. For example, 'It bothers the company' would be Это мешает компании.