Halacha requires placing the Tefillin Shel Rosh at or above the hairline, and aligned with the area in between ones eyes. Many people have the practice of using a small mirror to check the placement of the Tefillin Shel Rosh and ensure that it is positioned in the proper spot on the head.
Rabbi Hayim Halberstam of Sanz (Poland, 1793-1896), in his work Dibreh Hayim, strongly condemned this practice, and called it a "Minhag Borut" a custom of foolishness. He wrote that there is ample space on the head where the Tefillin Shel Rosh may be positioned, and thus a person can rest assured that he has placed it properly without looking in a mirror.
Presumably, the Rabbi of Sanz opposed this practice due to a Halacha that forbids men from following the fashion practices of women. Just as a man may not dress as a woman, similarly, he may not groom himself in front of a mirror as women customarily do.
Hacham Ovadia Yosef, however, rules that nowadays, when it has become commonly accepted for men to use mirrors for grooming, the use of a mirror is no longer identified specifically with women. Hence, it is entirely permissible for a man to use a mirror for grooming, certainly for the purpose of ensuring the proper observance of the Misva of Tefillin. Hacham Ovadia adds that Torah observant Jews bear the responsibility of appearing neat, clean and well groomed in order that they bring honor and admiration for the observant community. Appearing disheveled defames the Torah world, and it is therefore permissible and in fact desirable for religious Jews to use mirrors to ensure that they are properly groomed.
Thus, one may use a mirror to check the position of his Tefillin without any concern.
An interesting story relevant to this Halacha is told of Rabbi Shneur Zalman of Liadi (Russia, 1745-1813), the first Lubavitcher Rebbe, who once received a snuffbox as a gift. The Rabbi noted that the nose is the only part of the body with no desire associated with it; a person does not have an innate desire or impulse to smell pleasant fragrances. He thus looked askance at this gift, the snuffbox, which encourages a person to indulge in smelling pleasant fragrance, and thus lures the one part of the body he thought he did not have worry about toward indulgence. He therefore took the spices out and used the silver of the box as a mirror with which to check the position of his Tefillin, figuring that he should at least use some part of the gift for a Misva.
This demonstrates that even a towering Rabbinic figure used a mirror to ensure that his Tefillin was properly positioned, and this is, indeed, a proper custom to follow.
Summary: Many people have the custom to use a mirror to check that the Tefillin Shel Rosh is positioned on the proper spot on the head. This practice is entirely permissible and even commendable.
