Incompetence
This may apply to the subject and object of the inheritance. For example, if the legator is a fraudster, a criminal, and the legacy come from that activity.
It also falls into this category if the testator or heir is an unbeliever, since they cannot be subjects of the inheritance procedure according to the Sharia law. Incompetent is the person who is a subject of restriction of rights (Hajr), i.e., is under criminal proceedings, is in prison, has no free will, is in a mental institution, etc. In the latter case, the guardian inherits.

Murder
The killer cannot inherit from his/her victim. The point is the premeditated homicide in this case. If the husband kills his wife, he loses his right to inherit. The victim, on the other hand, can inherit from the killer. This is because with murdering, the killer becomes restricted, his/her assets is to be treated as an inheritance and the family of the victim can demand the redemption in cash or other form. This effectively transforms into the victim’s legacy, which is inherited by family members.
Unintentional, negligent homicide does not preclude heredity, but this must be established separately in each case.

Difference in religion
No one can inherit from a Muslim but a Muslim. Islam is not just a faith but a legal relationship. If one becomes a Muslim by birth or by converting the faith, he/she also confess his/her obligation with Islam as far as legal conditions are concerned. Those who are not subject to that legal relationship cannot enjoy the benefits and allowances arising from it. Thus, neither a Muslim can inherit from a non-Muslim nor a non-Muslim can inherit from a Muslim.
If the testator party of a married couple is a Muslim and he/she dies and his/her non-Muslim heir converts Islam after his/her death, the spouse is not entitled to inheritance. If, on the other hand, he/she converted Islam before the death of the Muslim spouse, he/she is entitled to an inheritance. If the testator and heir do not belong to the legal bound of Islam, the inheritance procedure is conducted according to the norms of their own affiliation. The Islamic jurisdiction is involved only if the procedure also affects Muslim's property and law.

Belonging to the legal systems of different countries
If the testator and heir live in two different Islamic countries, this should not - in principle -, be an obstacle to the process of inheritance. However, the practice may be different.
If, on the other hand, only one of them is subject to Islamic law and the other is subject to local, secular law, this may be an obstacle in the execution of inheritance procedure according to Sharia law.
In this case, it is recommended to prepare in the country where secular law system is in force a notary deed that contains the division of the legacy according to Sharia law and to consider it as a will. If the division of legacy that way does not conflict with the laws of the country, this obstacle can be overcome.