I have noticed that when answering Baruch hu u’varuch Shemo there are many people who do no say all four words. They say one of many abbreviations of the phrase. It seems that most people do this as they have heard others saying it incorrectly. Is this issue addressed by the poskim and what, if any, issues are there to responding incorrectly?
ב"ה The poskim most certainly address the issue of saying Baruch hu u’varuch Shemo. It is brought in the tur in the name of his father the "Rosh"= Rabbeinu Asher who explains the reason for saying Baruch hu u’varuch Shemo is in response to the saying the name of Hashem as expressed in the Passuk (Devarim 32:3) "When I call out Hasem's name praise God for his greatness".( See Tur and Shulchan Aruch 124) The Kabbalists also attributed great importance saying to Baruch hu u’varuch Shemo correctly. (כף החיים סי' ה ס"ק יב.) Unfortunately as you said many people say it incorrectly because of the way they have it heard it from others. When you think of it, it's one of the few parts of prayer which everyone knows you are supposed to say it, but it most siddurim it is just not printed. So people without giving much thought to what they are saying continue to say it the incorrect way and some others swallow their words since they are not used to speaking in Hebrew. What you can do is bring it to the attention of the Rabbi in your synagogue so he can then bring to the attention of the community. You can also enunciate your Baruch hu u’varuch Shemo so that others can hear from you when it is said articulately . Kol tuv.