sam2, rabbiofberlin — That is correct. A tallis is a tashmishei shel mitzvah and therefore a tallis bag *could* be used to keep a mirror, business card, siddur, printed chumash, tzedaka money (weekdays!)
A side note — While tefillin has extremely high level of kedusha, it should be noted that even the Tefilla shel yad has lesser kedusha than the Tefilla shel rosh and therefore, there are guidelines about how they should be stored in tefillin bags, aside from the issue of which tefilla should come out first during the donning proccess.
Back to the mirrors issue — Every shul (frum of course) that I have been to has mirrors in the men’s washroom. I seriously doubt they are been used to check tefillin!