The admissions consultant outlined what makes a thorough application package, unrespective of financial hardship.
What is the ERROR in this sentence?

The word "unrespective" is not a word. The word "irrespective" means "without regard for" or "in spite of". In this sentence, the admissions consultant is saying that the financial hardship of the applicant should not be a factor in determining whether or not the application is thorough.

The correct sentence should read:

The admissions consultant outlined what makes a thorough application package, irrespective of financial hardship.