The author should have added more information on his exceptional qualifications. Although the letter is not arrogant and boastful, one thinks that it lacks depth. The author did not mention any outstanding accomplishments which will make him stand out among the applicants. It was however written in a concise, professional and confident manner.
The letter did not specify what specific contribution the author can give to Big Four. The author failed to detail what value he will add to Big Four and why it will be advantageous for the company to hire him instead of the others.
The author did not give his available time for an interview. He just mentioned when he will call to request for an interview. It would have been better if the author already attached references to his resume instead of stating that the company is free to contact his former employers. This could have given the impression that he is open and confident that his former managers will give him good feedback.