Why does the DHC-6 pitch down when the flaps are retracted, rather than up? Air Moorea Flight 1121 crashed because one of its elevator cables broke immediately after the pilot retracted the flaps, but before he could trim out the resulting pitch-down moment - to quote the English translation of the BEA report,

The operator called for the reduction in engine RPM before retraction in order to mitigate the pitchdown moment caused by the flap retraction and so that the right hand, after having positioned the flap control lever on 0°, could be placed be placed on the elevator trim in order to reduce the effort on the control column. [report page 17/PDF page 19]
...stick free, the flap retraction led to a pitch-down moment varying the aeroplane trim between 20° and 30°, the rate-of-climb indicator going to stop at less than 3,000 ft/min and speed reaching 140 kt in twenty seconds… [page 42/44]
In flight, the loads on the cable are at their greatest when it is necessary to counter the pitch moment induced by the retraction of the flaps. [page 61/63]
The malfunction occurred at the top of the initial climb, passing through 350 feet, when the pilot retracted the flaps then adjusted the engine parameters. While he was adjusting the parameters with his right hand, he was holding the wheel with his left hand while pulling back to counter the pitch-down moment and stabilise the airplane on its flight path. It was only at the end of this process, which lasted nine seconds, that he would adjust the trim.
[...]
The flight tests showed that during flap retraction, when pitch control is free, the airplane dives with a high pitch angle. [page 63/65]

and, finally,

The DHC6 Twin Otter has significant pitch-down moment when the flaps are retracted. [page 67/69]

How can this be?  Flaps extend downwards from the trailing edge of a wing, and, thus, should always produce a pitch-down moment when extended (like applying nose-down elevator, except with a much shorter moment arm), and a pitch-up moment when retracted.  Why is the DHC-6 different in this regard?
The Twin Otter isn't unique.  Flaps have varying effects on different airplanes.  Some pitch up with flaps extended, some pitch down.   The pitching moment from flaps isn't just from the nose down moment from the increase in airfoil camber; it includes effects of increased downwash on the tail, which creates a pitch up moment, and to some degree, changes in the vertical aerodynamic center resulting from adding drag up high or down low (like the mild pitch down moment caused by gear extension).  

In the Twin Otter the double-slotted flaps are extremely powerful and create a very strong downwash increase at high angles as opposed to just mostly turbulence you get with simpler flap setups. The result is the net effect of flap extension, with the high wing and the location of the horizontal stabilizer, is pitch up because those forces are stronger than the nose down moment created at the wing itself by the camber change.