The Shulhan Aruch (O.H. 124:8), based on a discussion in the Gemara (Berachot 47a), says that “Amen” should not be recited in a manner that is “Hatufa”, “Ketufa” or “Yetoma”. Hatufa, or hurried, means that one does not vowelize the letter Alef with the Kamatz and thus pronounces it “‘men”. Alternatively, it means that one hurries to respond Amen before a blessing is completed. Ketufa, or plucked, means that one does not properly pronounce the final Nun and says “Ame’”. Finally, Yetoma, or orphaned, means that one answers Amen to a blessing that one is obligated in but did not hear. For example, if one knows that the blessing for the Shofar is being recited but does not actually hear it, but answers Amen anyway. The Rama (ibid.) adds that there is a stringent opinion the Amen Yetoma also applies to blessings that one is not obligated in. The Abudraham writes that Amen Yetoma is when one does not respond Amen immediately after a blessing, but rather waits a little, such that the Amen is orphaned, as it were, from the blessing.
Rabbi Ben Zion Abba Shaul (Or Lezion, vol. II, ch. 5, § 16) clarifies that the Shulhan Aruch does not follow the strict opinion of the Rama and that only responding Amen to a blessing in which one is obligated but did not hear is considered Yetoma. Nevertheless, the Ben Ish Hai (Od Yosef Hai, Parashat Vayehi, §19) is of the opinion that since the Gemara (ibid.) says that a person who is accustomed to recite Amen Yetoma will have orphaned children, he also takes the strict approach and says that one should not answer Amen to a blessing that one is not obligated in and does not actually hear. Similarly, Rabbi Baruch Toledano (Kitzur Shulhan Aruch, 111:37)writes that one should never respond Amen to any blessing that one does not actually hear.
Interestingly, the Gemara (Sukkah 51b) recounts that there was a synagogue in Alexandria, Egypt that was so large that attendants had to wave flags in order to notify the congregants when to respond Amen. This would seem to contradict the ruling of the Gemara. The Gemara clarifies that since everyone knew which blessing was being recited it was not considered Yetoma. Based on this, Rabbi Ovadia Yosef (Yechave Da’at) writes that one may answer Amen to a blessing that one hears over the radio.
Summary: One should pronounce Amen properly. One should not respond Amen to any blessing that one does not hear.