Ahmad Shah Abdali's nose had fallen off due to cancer or leprosy by the time he came down to India in 1761. He wore a diamond studded nose. This is not shown in the movie.
Raja Suraj Mal did not go away on his own. He went away because Sadashivrao Bau tried to have him assassinated despite reassurances to Raja Suraj Mal by the others in the army (Holkars and Scindias) that no revenge would be attempted. Holkar and Scindia alerted the Raja of the decision and he fled in the middle of the night to the safety of his fort.
Sadhashivrao Bau was not the diplomat he is shown to be. He was arrogant and often disregarded the good advise of others around him. He bogged himself down with close to 1 lakh civilians who literally ate out all the reserve supplies. He made enemies in several places through his highhandedness in dealings. He foolishly (some might say bravely) left his post when he could have won the battle by staying on his elephant. The army needed their leader more than Vishwasrao and not seeing him in place they panicked and ran helter skelter. This was another reason for the defeat of the Marathas in Panipat.
Mahadji Shinde is left out of the movie though he took part in the Third Battle of Panipat.