It really depends on what kind of insects you want to capture, as all methods have their biases. Pitfall traps probably won't work in a mangrove forest if the ground is waterlogged. Beating the foliage with a sheet below to catch the fallen insects would be a good way to collect insects and have information on the plant species they came from. Flight intercept traps are good for catching flying insects, and you can also get an approximate measure of the direction in which they are moving, so you can know whether they are entering or leaving the forest.

It absolutely depends on what ecological or taxonomical group you plan to study. 

Malaise traps (will be hard to put them in mangroves)

Light traps (may attract species from outside the mangroves)

Sweep netting on canopy of mangroves - good one

Flight interception trap (like window traps or polytraps) - surely also good ones

in addition to Dmitry's reply, one could add (1) "fogging" the canopy and trunks of the mangroves with insecticide and also (2) baiting (e.g. rotting fruit / rotting fish / pheromone traps / mothing "sugar"). For some groups, line transects or fixed point transects of traps or observation points could be established (e.g. butterfly transects).

For light trapping, the type of light source used will affect the catch and likelihood of attracting species from outside mangrove habitat, though the size of the habitat itself will also affect the catch radius (not to mention moon phase, weather, height above mangrove "floor" of the light source....).

Determining which insect species are resident within the mangrove and which are only utilising the mangrove for a particular resource (e.g. pollen) isn't easy as the assemblage of insects will be great and cover many orders, never mind families, so complete assessment will take much effort, and probably all of the methods suggested, over at least a two year period (preferably longer to account for variations in weather caused by short term climate patterns, such as El Nino). For species that exhibit specific phenological patterns or are affected by lunar periodicity, repeat surveys must be timed accordingly to effect sufficient sampling.

Hope this helps.

Take a look at the classic work of Simberloff & EO Wilson in mangrove islands of Florida Keys.  Especially: Wilson, E. O., & Simberloff, D. S. (1969). Experimental zoogeography of islands: defaunation and monitoring techniques. Ecology 50:267-278.

Thank you for all your responses. So much appreciated, will consider your input and come up with a proper method based on your advice.