The sentence "Whom is most responsible for your department's recent achievements?" has a grammatical error.
1. The correct use of "whom" in this sentence should be "who." "Whom" is used as the object of a verb or preposition, while "who" is used as the subject of a sentence. In this case, "who" should be used at the beginning of the sentence to refer to the responsible party.
2. The corrected sentence would be: "Who is most responsible for your department's recent achievements?"
Therefore, the sentence with the grammatical error is "Whom is most responsible for your department's recent achievements?"