Mosquitos I doubt; they are so r-strategy that conditions (existence of pools of water in particular) count more than predation in population growth. (basically one mosquito can have so many offspring if conditions are right that the number eaten is irrelevant) (not that I'm not in favour of anything that eats mosquitos).
Furthermore, lots of different things eat mosquitos , both in the laval and adult phases. Spiders, birds, bats, fish, other insects; everything likes a quick mosquito, and it doesn't hold the population down in a wet summer.
Slugs, now - not enough things eat slugs, and they reproduce slower. You might get a temporary rise there (not that they aren't partial to wet conditions. Mind you, so are amphibians.) If the cane beetle from an earlier post has only amphibian predators its numbers could explode before a newbalance is found, ruining the economy of a small region (geographically speaking) Such things have happened in the past; humanity survives them.
Diseases with arthropod vectors are unlikely to rise to levels they have achieved in the past; too many different avenues of attack. And mankind survived those previous levels (yes, some of Africa was rendered unsuitable for herding by tzetze, but I don't think frogs would have helped much there)
If you want to be worried about insect vectors, worry about some fast-breeding species being carried in from some obscure corner of the globe in someone's souvenirs to somewhere it had no natural predators, carrying a disease it's never been considered worth studying and to which a significant percentage of the population have no resistance.
But even that has happened in the past (with considerable social disruption, 'tis true.)