* Draghi didn't have responsibility for punishing Monte Paschi * BOI vigilance is slow but deliberate - senior source * Says Monte Paschi vigilance did not fail, but would welcome more powers By Gavin Jones ROME, Feb 4 (Reuters) - Mario Draghi was informed of doubts raised by Bank of Italy inspectors about the Monte dei Paschi bank but had little control over what has been widely criticised as ineffective oversight of the scandal-hit lender, a senior BoI source told Reuters.