1. The weakest section of Ms. Jackson's letter is the conclusion.
The language used in the conclusion is not as formal as a request to a superior should be. The word choice makes her request sound too familiar and informal. Also, instead of presenting herself as available at all times to answer any questions the reader may have, she states that she will communicate in a week, making her sound too self-assured and even smug.
3. Yes, I would hire Ms. Jackson.
Ms. Jackson portrais very convincingly all her abilities and qualifications for the job. She provides good references and names of officers that will attest to her adequacy for the possition. She also shows herself as a respectful, well educated candidate which would convince me to give her the job.