Indian IB (or newly made RAW) was not capable enough to have conceived and executed all the subversion activities in East Pakistan that brought small amount of Pakistani Army to it's heels. There was a concerted effort from USSR which provided India all the planning to execute and foment unrest and militancy in East Pakistan.
When USA was stopping all the Military Aid, during every conflict, to Pakistan (for which it was the main supplier) and India (which had multiple suppliers) , USSR was selling arms to India at 'Cut-Price' to build a strategic allaince against USA and China. In both 1965 & 1971 wars Pakistan, at the end, was almost without ammunition to fight any further. That is why, most of the Pakistani arms industry - including the nuclear deterrence - has developed after 1971. This was the first positive lesson of the war - Never Again.
During 1965 war, Ayub Khan secretly visited China and met Chinese Premier Chou En-Lei who offered Pakistan unconditional support but also warned Pakistan to be prepared for a long war and be ready to lose even some major cities like Lahore. Ayub Khan was not ready for a prolonged war, so, he returned empty handed. Chinese could and must have offered their help to Pakistan during the 1971 crisis, but, the political leadership in Pakistan was more interested in saving their control of western half of the country; for which they were more than willing to lose East Pakistan (Udher tum, Idher Hum).
Same can be said about Military High Command too. After the humiliation of 1971 war, recruiting to commissioned posts from nobility decreased and a new breed of army officer appeared on the scence, belongining to middle classes and having close physical and emontional links with the rest of the population. That is why that same Dr. Mehboob-ul-Haq who had said during Ayub Khan's tenure that the welfare of the masses could get a rest while the capitalists make money was a totally changed man on his second term. During the next army regime - that of Zia-ul-Haq, as minister of planning Dr. Mehboob-ul-Haq brought a positive change to the status of middle classes. Infact, there was an entirely new class of Noveau Riche. We can argue that he got some influence from Military leadership which was more entrenched to the soild. That was the second positive lesson of the War - The welfare of the masses and a change in the mindset of the military leadership.
During 1962 war with China, when India's defences were shattered and Calcutta lay 300 undefended miles to take over, in a desperate attempt, Nehru pleaded to US to send Airforce for help - with Tactical Nukes if possible. Lucklily, China declared a unilateral cease-fire. It is also said that during 1971 war, US threatened to China that if it tried direct involvement in war, then, America will put all of it's weight in India's basket. Considering that Chinese financed Vietnam war was a big humiliation for US, America was restless to get even. If true, this confirms that USA wanted Pakistan to lose it's eastern arm. The mouth piece of US foreign policy - US media - was blatantly anti-Pakistani during the whole crisis. US also wanted Pakistan to change it's focus of attention from eastwards (Indiacentric) to westwards (West Asia centric), where it could be used as a vital ally against the onslaught of communism.
Indira Gandhi had stated that 'We have sunk the Two Nation Theory' in Indian Ocean; but it successfully floated in the creation of a sovereign 'Muslim Bengal'. Just becasuse they had a shared language, history, customs and culture, East Pakistan did not fuse with 'Hindu Bengal' and become a part of India. It remained as an Independant Muslim state; this was a vindication of Two Nation Theory for the second time. This is the third and final lesson learned from the war of 1971 - The Muslims of sub-continent are a separate nation and no force, no ideology and no (Wannabe) Superpower in the world can change that fact!
