There is nothing wrong with a man using a mirror, even l’chatchila, because the halachos of men not beautifying themselves as women do are subject to societal norms, and where it is the norm to do so, it is fine – see R’ Akiva Eiger at the end of YD 182.* The Ran (AZ 9b b’dafei haRif) is quoted as saying that the “?????” withhold themselves from doing so in any event, but ??? ??? ??? ??? ???.
As Sam writes, looking in a mirror is not necessary for tefillin.
*http://hebrewbooks.org/pdfpager.aspx?req=9146&st=&pgnum=252&hilite=