Electronics and age do not cause fires. Defective designs cause fires. Protective standards (ie UL) exist for this reason. Unfortunately, power strips with protector parts have a higher rate of fires. Yes, these occur rarely. That means fire happens too frequently for operation on a ship.
How dangerous? Learn from a nationwide 'remove them all immediately' warning from the CPSC.
http://www.cpsc.gov/en/Recalls/2014/Schneider-Electric-Recalls-APC-Surge-Protectors/
Aged wiring will degrade and cause the insulation to become brittle. See the excerpt from the NFPA below. My final word on the extension cord saga.
"Residential wiring can be classified into two groups, behind the wall (fixed)
wiring and portable wiring (appliance cords, extension cords, etc.). Each class can
have its own set of circumstances that can lead to potentially hazardous conditions,
including damage, misapplication, loose connections, harsh conditions, and wire
aging. Some examples for fixed wiring arcing failures include loose connections at
an outlet, a staple or drywall screw bridging conductors, and excessive self-heating
by current flow leading to wire insulation degradation and failure. Examples of
portable wiring faults include cut wires, broken strands, abraded wire insulation,
loose connections, and self-heating. All these conditions can occur for old as well as
new wiring. Aged wiring and in particular fixed wiring, since it is much more costly
to replace than portable wiring, may fail due to insulation degradation, especially if
rework or retrofitting has disturbed the wiring. Moving and bending old wiring
that has become embrittled from age, can crack the insulation and expose
conductors possibly leading to arcing."