In some places mosquitoes carry some extremely damaging diseases so I can understand the push to control them but this ignores two things:
1. Mosquitoes are an extremely important food for a large number of animals.
2. Most means of removing mosquitoes affect a wide range of unproblematic animals - in Africa DDT is frequently used to control malaria (and this insecticide is very harmful to other animals) and even the 'less damaging' insecticides used in the US and elsewhere tend to wipe out many unintended animals. Attempts to control West Nile Virus, which affects a handful of humans a year, have decimated helpful insects, shellfish, and negatively affected the animals that eat them.
I do not have a problem with trying to remove a specific virus or bacterium like smallpox or polio, but I don't support the purposeful extinction of more complex lifeforms.
I agree with point #1, they are a vital part of many food chains so eradicating them would cause widespread and uncontrolled changes in many ecosystems which could in turn lead to mass extinctions of several other species (a domino effect).
For point #2, while there are many dangerous pesticides out there, DDT is not one of them. The only known effect of DDT on non-insect species is that high doses (much higher than would ever occur during normal use of the chemical) have been linked to a thinning of egg shells in predator birds. This thinning could contribute to up to a 1% decline in predatory bird birth rates. Most commonly known information regarding DDT is false and is the result of reactionaries who are opposed to any human interference in our own ecosystem. In fact, DDT is less harmful than most pesticides that are used on a daily basis here in the US, but reactionary legislation still prevents a safe chemical like DDT from being used.