Mercury and Venus are, respectively, the first and second planet from the Sun.

Correct sentence: Mercury and Venus are, respectively, the first and second planets from the Sun.

In this sentence, there are two nouns: Mercury and Venus. Taken together, "Mercury and Venus" is a plural noun (which is followed by the plural verb "are"). The word "planet" modifies both Mercury and Venus, and should also be pluralized as "planets."

The flowers were put in the holder and situated throughout the office.

Correct sentence: The flowers were put in the holders and situated throughout the office.

We know from the sentence that there is more than one flower in the apartment. The word "holder" is related to the word "flowers" and should also be plural, otherwise, it would be illogical that one flower holder could be spread throughout an office.

Over time, the workers have developed tactic to finish the work faster.

Correct sentence: Over time, the workers have developed tactics to finish the work faster.

In this case, the collective noun "workers" can either be paired with "has" or "have." However, the noun "tactic" must be written in the appropriate number in context of the sentence. "A tactic" would signal a single procedure, where "tactics" would signal many.