Shevet HaKehosi: Can You Be Yotzei With A Bracha From Someone Who Doesn't Speak Clearly?
The Shulchan Aruch says (OC 53:12) that someone who has a speech impediment and cannot, while reading, correctly differentiate between the letters Aleph and Ayin should not be a Chazan. Although we cannot differentiate between these letters it is permissible to be a Chazan since this Halacha doesn't apply if everyone has the same problem. What is more problematic however is some who cannot properly pronounce the letter "Shin" and reads instead "Sin". Another example is someone who cannot properly pronounce "Ches" and instead reads "Hey", or someone who slurs and swallows words.
The Mishna Brura brings the Pri Chadash who holds that if there is no one who is more qualified to be Chazan than the person with the speech impediment can be the Chazan. However this is only a temporary solution. Such a person cannot be appointed as the official Chazan. The Pnei Moshe disagrees and says such a person may not be Chazan even occasionally.
From here the Shevet HaKehosi (5:30) concludes that if someone needs to be yotzei with a bracha he should try to find someone who speaks clearly. Only if they cannot should they rely on listening to a bracha not pronounced clearly.
Disclaimer: We try to convey the Tshuva to the best of our ability. We admit that our understanding may not be accurate. Please also understand that this Tshuva may not be the final word on this topic. One should consult a Rav before drawing any conclusions.