Visa Integrity and Security Act of 2001 - Expresses the sense of Congress, in light of the September 11, 2001, terrorist attacks against the United States, that the Attorney General should: (1) implement the integrated entry and exit data system; and (2) establish the Integrated Entry and Exit Data System Task Force, which shall focus on biometric technology and tamper-proof identification, and integration with law enforcement databases.

Amends the Immigration and Nationality Act to: (1) direct the Attorney General and the Federal Bureau of Investigation to provide the Department of State with access to specified criminal history records in order to determine whether or not a visa or admissions applicant has a criminal history; and (2) include specified passport-related requirements as part of the visa waiver pilot program.

Amends the Illegal Immigration Reform and Immigrant Responsibility Act of 1996 to expand the foreign student tracking system to: (1) include "other approved educational institutions" (including flight and language schools); and (2) require university reporting of student failure to commence studies.

Requires an employer who terminates the employment of specified aliens (H-1b visa) to so notify the Attorney General.