Ineffective Assistance of Counsel
An ineffective assistance of counsel claim means that your attorney was ineffective--in other words, he didn't represent you professionally. But an ineffective assistance of counsel claim doesn't just require you to show that your attorney was ineffective or made unprofessional errors. You also have to show that he or she was so ineffective that instead of helping your case, your attorney hurt your case. Ineffective assistance of counsel claims are by far the most common kind of habeas claims.
This kind of claim usually involves what's called a Brady violation. A Brady violation occurs when the prosecutor fails to turn over several different kinds of evidence. The first example of a Brady violation is when the prosecutor fails to turn over evidence that would tend to show that you did not actually commit the crime. Another example of a Brady violation would be if the prosecutor doesn't turn over evidence that would show that you are less culpable for committing the crime. A third kind of Brady violation is when the prosecutor fails to turn over evidence that tends to show that the prosecution's witnesses are less believable than then otherwise appear. They might be less believable because they have a lengthy criminal record or they've entered into an agreement with the prosecutor to get a lighter sentence in exchange for testifying against you.. Another phrase for this kind of evidence is impeachment evidence.
Conflict of Interest
A claim for conflict of interest can arise when your attorney represents a co-defendant or a witness in the case. Sometimes your interests and your co-defendant's interests are very different. Another example of conflict of interest is when your attorney has a financial conflict with the case. Another example might be that your attorney's license to practice law had been suspended when he was representing you.
Failure to File a Timely Appeal
It is your decision whether or not to appeal your case. Your attorney can give you advice about whether you should or not, but ultimately, it's your decision. A common habeas claim is when an attorney simply fails to file an appeal in time and the appeal is denied because the attorney missed the filing deadline.