Q. If I hear someone make a bracha, perhaps the chazan in shul, and he mispronounces Hashem’s Name as is unfortunately common, either by saying Adinoi or Adeenoi, instead of Ado-noi, I have four (see next shaile) questions:

1) Is one obligated to say Omein at the conclusion of that bracha?
2) If he is not obligated, may he answer Omein at the conclusion of that bracha?

A. Shulchan Aruch (O.H. 215: 2) rules that one is obligated to answer omein after hearing a brocho. How much of the brocho he has to listen to in order to answer, is debated by the Poskim. Mishna Berura (ibid. 6) seems to agree with the opinion (Eliahu Rabba and Chaye Adam) that just listening to the end qualifies, as long as one knows what brocho was said.
Shulchan Aruch (ibid. 4) also avers that when reciting an unneeded brocho (and obviously one in vain), no omein should be answered. Biur Halocho (ibid.) maintains that when in doubt answering omein is not obligatory, but could be said.
Mishna Berura (214: 4) also maintains that even if one omitted totally one of the two names of Hashem recited in most brochos, he complies with the brocho after the fact. In Shaarei Tzion (ibid. 2 and 3) he further explains that even mentioning one of the other seven names or a name in another language is also bedieved enough.
Piskei Teshuvos (1: 5: 6) quotes from Nimukei Orach Chaim, that although one should be very careful to pronounce Hashem’s names correctly, articulating the daled of A-doinoi with a chirik, sounding as A-dinoi, may be acceptable after the fact.

Horav Shlomo Miller’s Shlit”a opinion is that all individuals, but specially the sh’liach tzibur should see to pronounce properly every word of the tefila and particularly every one of Hashem’s names, however, in your case, omein should be answered, since one complies with the brocho after the fact.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a