Not exactly true about the wings falling off!! See this quote from an article on that very problem.
"Early Mosquitos were assembled using casein glues, which were exactly what you can buy today in any hardware store under the rubric “woodworker’s glue.” Casein glues are milk byproducts (which is why the most common brand, Elmer’s, has the familiar cattle-head logo), so they provide munchies for microorganisms, particularly when the environment is wet and warm, as was the case when the first Mosquitos were sent to Southeast Asia. In the Pacific theater, some Mosquito glues turned cheesy, and upper wing skins debonded from the main spar.
The solution turned out to be two-part urea-formaldehyde glue, which de Havilland began using in the spring of 1943. The urea glue was applied to one wooden surface and the formaldehyde catalyst brushed onto the other. When the two were clamped together, in some places with the simple pressure of tiny brass brads, a waterproof bond stronger than the wood itself was formed."
Whist not completely obviating the unique problems caused by the Mosquitoes wooden construction once Glue was changed and as long as the interior was kept dry, then they were quite capable of working well in the tropics.