It doesn't take an expert to tell you that if a power supply is smoking, that's a bad sign. But as an expert, I'm telling you that if a PSU is smoking, that's a bad sign.
Without analysis it can be difficult to tell what exactly burned... But every component in a PSU has a purpose, and if a component burned then some feature of the PSU's design is no longer functioning as intended. Maybe that feature has a small effect on the PSU, maybe it has a large one. Regardless, I would not use it.
Smoking PSUs reminds me of an unrelated story from when I was dicking around with an ATE in Taiwan. Did you know that when you pour liquid nitrogen into a PSU you can get some really interesting effects? The LN2 lowers the temperature of the components in the PSU, and lower temperature means lower resistance. This means less energy lost to heat! Because of that the PSU's efficiency actually increased from around 80% to around 88%. Also, since there was less voltage drop in the components, the output voltage increased from +12.1V to +14.2V! I actually tripped the over voltage protection (OVP) a couple of times, which is rare. Now I'm not sure what affect extreme cold has on electrolytic capacitors, but I'm sure it can't be good. I didn't have an oscilloscope hooked up, but it would not have surprised me if the scope screen were going wild.
The PSU actually lived quite a long time under this abuse (It was a Delta Electronics 200W unit, a very well-built SFF PSU), until finally I ran out of LN2 and the ice inside the PSU melted to water and caused a number of shorts that fried the PWM controller.
That Delta 200W PSU was a tough one, very well built for such a diminutive unit. It provided its rated wattage in spec reliably with good voltage and ripple, the OPP reliably shut it down at 225 - 230W load to prevent overloading, it survived even when I stopped its fan with a pen and covered it with a box to trap the heat for 12 hours overnight; temperature inside the box reached 55*C, no shutdown or failure. It even survived the LN2 torture until the ice melted. I like Delta. They're a good company and they deserve a bit more respect from the IT community.