What is the failure mode for a power supply being incorrectly set for 110/240v using the switch?
The switch changes the power supply configuration from a full-wave bridge (open) rectifier to a voltage doubler (closed). The main DC supply rail is normally ~300VDC when the switch is in the proper position for the supply voltage. 

Doubler (120VAC) - the output is peak \$2\cdot 120 \sqrt{2} \$ = 339V

Full wave (230VAC)- the output is peak \$230 \sqrt{2} \$ = 325V

Average will be a bit lower than the peak. 

(Component designations refer to the partial schematic below). If you have it plugged into 230V and switched to the 120V setting (SPST switch S1 is closed) it will attempt to create about a 600V+ rail, which will kill the main switching transistors (Q1 and Q2) and possibly the main capacitors and other parts if the fuse does not blow fast enough. The transistors will fail shorted and short the main bus, causing high current to flow, blowing the fuse with a pop. 

Each main filter capacitor C5 and C6 is rated at (typically) 200VDC and they are connected in series, so 400V is the maximum.  

Typical schematic (partial) of such a supply from here: