There are two general types of smoke detectors in use for everything from residential to commercial to aerospace applications; ionization and photoelectric.
This type has two chambers, a sealed control chamber and an open chamber. The air in each chamber is ionized using a radioactive material and a difference is detected when smoke enters the open chamber.
This type monitors the changes of reflected light intensity caused by smoke particles. This model also includes a heat detector which triggers when temperatures in excess 100°C are detected.
Ionization and photoelectric respond to different types of smoke slightly differently, but in the confined space of the lavatory, smoke detection should be more than an adequate with either type.
The CRJ lavatories have either a Jameco PU-90 Series, or Kidde M3000 Series
All cargo compartments are equipped with smoke detectors as well.
While a nuisance in a home, a false fire indication in an aircraft may spur immediate action such as emergency descents, diversions, and evacuations causing disruption, injuries, and elevated general hazard.
A study of nuisance smoke detections in aircraft 1974-1999 (FAA Technical Note 00/29) found the incidence of nuisance to verified smoke events was as high as 200 to 1 during 1995-99.
"Fire Detection for Aircraft Cargo Compartments, Reduction of False Alarms", Philippe Mangnon(pg 653 of NIST 965) investigates a comprehensive list of possible causes. It shares an interesting case where a cargo compartment smoke detector was triggered from condensation caused by a load of warm fruit. Another case was eventually tracked down to excessive oil particles in the cabin air system due to an oil leak in the APU.
The paper compiles a comprehensive list of all potential sources of nuisance alarms: moisture/condensation (including origination sources of fruit, animals, and vegetables), oil, fog, exhaust gas, sand, and dust.
The CRJ maintenance manual also mentions operation of a mobile receiver in close proximity of the detector as a source of false alarm.
The manufacturers of residential smoke detectors seem to suggest dust as the leading cause of nuisance alarms in homes and recommend regular cleaning (What to Do If You Have a Nuisance or False Alarm).
Even if these sources aren't enough on their own, they can add up. A dirty detector may increase it's sensitivity priming it to alarm at a level of humidity a clean detector may not.