Final answer:
The item hanging next to the file cabinet that led Dan to suspect there was a deeper significance to the cabinet's placement was a mysterious note.
Step-by-step explanation:
The item hanging next to the file cabinet that led Dan to suspect there was a deeper significance to the cabinet's placement was A mysterious note. In the given passages, there are mentions of a trumpery fillagree card-rack, a large writing-table, and a savings' bank, but none of them indicate any suspicions related to the file cabinet. However, the mention of a mysterious note suggests that it may contain important information or a hidden message.