The Shulchan Aruch writes (OC 215:2) that one should not respond amen to a bracha recited by an adult Jew if שינה ממטבע הברכות he changed the way the bracha was coined. The Mishna Berura there notes that this is due to the fact that if he changed it too much that he would not fulfill his obligation, it is then a bracha levatala to which one is forbidden to recite amen (per OC 215:4).
How much of a change is considered שינוי מטבע? The Rambam (Brachot 1:5) defines the minimum as a mention of "God's name, His Kingship, and the notion of the bracha." For instance, the Shulchan Aruch rules (OC 167:10) that if instead of HaMotzi, one said "Blesses is God the King who gave me this bread" he has post facto fulfilled his obligation, even though he changed the text of the bracha (and I mean content-wise, not because of the translation). So as long as they pronounce enough words correctly that they still have imparted the proper "notion," they have fulfilled their obligation and you may recite amen. (I recognize that this is a little vague, but there is no way the texts can cover every possibility. One has to be aware of the meanings and potential differences in similar sounding words, just like the one correcting a ba'al keriyah.)
As for how clearly you need to say a word for it to be considered the word you wanted, see my answer here where I discuss the matter and conclude that you have to actually say the correct phonemes, and the only wiggle room is with "minor" differences like shva na' and separating similar consonants (like in the phrase "black coat").
Finally, if you are alone and your silence would be noticeable, I can personally recommend using the old "amem" trick to avoid any bad feelings.