What are some examples of reversible errors in the situation described below?
As a general rule a different attorney is appointed to serve as the appellate counsel in a case where an indigent defendant has been convicted, but a defendant who retained his or her own counsel may continue with the same legal representation. When all appellate efforts have been exhausted, the defendant may decide to pursue a writ of habeas corpus if the conviction occurred in a state court.
From the description that you have offered, I do not see reversible error. It is not at all uncommon for separate counsel to represent indigent defendants simply because that attorney may specialize in appellate practice. Trial attorneys representing indigents are often quite busy and an appellate assignment might well be unduly burdensome. A defendant who has retained his own counsel is by no means obligated to continue with that counsel through appeal. He may retain appellate counsel if he wishes, since he is responsible for the cost; or he may remain with his trial counsel who is familiar with the case. It is not unusual for defendants to retain separate counsel for appeals simply on the basis of the appellate attorney specializing in that practice.
As far as the writ of habeas corpus that you mention, I assume you mean allegations of ineffective assistance of counsel. These have become almost routine, although they should not be. They occur most often in cases of appointed counsel because it costs the defendant nothing to pursue the issue, and there is a perception--incorrect in most instances--that appointed counsel is second hand counsel. Retained counsel are just as apt to make mistakes as appointed counsel, and the latter will not treat the case as a bothersome afterthought. Any attorney who does so is subject to severe sanction which he does not wish to face.
So to answer your question, from the facts presented, I frankly do not see reversible error. Post conviction relief is more often than not the result of a defendant unhappy with the outcome rather than a genuine failure of counsel to represent him adequately.