When the LVPD officer stops Roy Logan after he leaves the bank, he notices what looks like blood on Logan's hands. Yet the bank teller and manager in the previous scene apparently never noticed the blood, despite having numerous opportunities during the hour they spent with him, including several close views of his hands (such as when he presented his driver's license). When he was in the bank, blood was also not apparent to viewers, so the makeup department must not have added it during that scene.
Doc Robbins stated that the girl was dead when the finger was severed, yet the brief scene showing the finger being removed shows blood flowing. A body would not bleed from such a wound. Blood flow stops when the heart stops functioning.
The kidnappers voice is altered by the inhalation of helium, as we see him breathing from a small container later found by Grissom where the ransom money was delivered. However, the helium only will alter the voice for a short time- maybe a breath or two. The kidnapper seems to be able to sustain the effect for extended conversations without breathing any more.
The head of a crewman can be seen reflected in a mirror/window on the left-hand side of the screen just as Nick is beginning to make his way through Logan's townhouse to investigate it.
Sarah says the finger is severed 'just below the right intercostal joint.' Costal refers to ribs, so such joints are not found in the finger. The finger was actually severed at the metacarpal phalangeal joint.