The suspected killer would not have been in custody for very long. As it is subsequently shown, the victim was shot from a different direction, and the entry wound would have shown that he wasn't shot from where the alleged shooter was located, not to mention any bullet holes in the victim's chair. Also, the suspect would have had no gunpowder residue on his hand to show he had shot the gun. (If he had run away he would have been a more plausible suspect.)
Twice when the alarm bells ring in Faber's (Woodrow Parfrey) office, the clapper arms can be seen up close, and they are not moving.
When Mel Faber (Woodrow Parfrey) is giving Mannix a demonstration of alarm systems, as Mannix triggers the second alarm, a boom mike can be seen coming down from the top inside the doorway.