Mulder refers to a cross hanging in what is usually considered an inverted position as being a "protest, a sacrilege against the Church". In Roman Catholic symbology, an "inverted" cross is known as the Cross of Saint Peter. Later in the episode, Scully gives an alternate interpretation referring to a legend that when Peter was martyred, he asked to be crucified head down because he was unworthy to die in the same manner as Christ.
Mulder's interpretation usually refers to an inverted crucifix, a cross with the image of Christ being crucified. An inverted cross without Christ fits Scully's description, also known as a Petrine Cross.
Dara died and was autopsied by a county coroner. However she died in Alexandria, which is an independent city not part of any county.
During the autopsy, right after Scully believes she has seen Emily, the camera goes back to the dead girl who moves on the autopsy table.
The seraphim are described as having four faces; those of a lion, ox, eagle, and man. This is incorrect, as cherubim have four faces; seraphim only have one, which is covered by a pair of wings.