It says in the Midrash that when one hears another pray for something good, or hears him bless another Jew, one must answer Amen. This even applies to a blessing which does not include G-d's Name. That is why we answer Amen to each Harahman in Birkath HaMazon.
If one has just said a Berakha (blessing) before eating a food, or performing a precept (Miswah), and hears someone else recite a blessing, one may not answer Amen between one's own blessing and eating the food or performing the precept. One should only answer Amen after one has eaten the food or performed the Miswah in question.
If the one reciting the blessing stuttered in the wording of the blessing, or skipped over the portion of Shem Umalkhuth (G-d's Name and Kingdom), one does not answer Amen. The reason is that it is not considered to be a blessing.
(See Kaf Hahayyim, 215, Oth 11, 13, 15)
Kaf Hachaim, Kaf Hahayim, Kaf Hahaim, answering amen to a bracha