Could an explosive decompression trigger the smoke detectors?
In an explosive decompression the cabin air may fog, this is because of rapid cooling causing the moisture in the air to condense. How thick it is and how long it may last depends on a number of factors. 

There are two types of smoke detectors, these are optical particle detection devices and ionization devices. Both types are used on commercial aircraft, some detectors have both methods built in.  Ionization devices are tripped by changes in the electrical conductivity of the air flowing through them and are not very sensitive to steam. Optical smoke detectors work on a different principle, detecting light being scattered by particles in the air. Optical devices are susceptible to false readings from moisture, in fact manufacturers of home devices recommend they are installed away from bathrooms to avoid false alarms. 

However, airplane certified units are designed and built to a very high standard, the FAA states in the Aviation Maintenance Handbook that requirements for fire protection systems include:


  No false warnings under any flight or ground condition.


So it is very likely that the manufacturers have taken steam into account, after all cabins sometimes fill with steam when the air conditioning has been turned on when if the air is very moist. An extreme example is this flight at Shenzen. That did not set off smoke alarms, and although I've never seen it that bad I have personally been in the cabin when it's noticeably filled with steam and there were no smoke alarms. 

So yes, the cabin can fill with steam in an explosive decompression, but it is unlikely - but possible - that the smoke alarms would go off.