How to get rid of a few mosquitoes/gnats that constantly sneak in?
Beyond visual inspection to find obvious holes, you can do a blower door test to find the source of leaks. I had one done as part of an energy audit (rebate program the government was running). You should be able to find an inspector in your area that offers this service, rent the equipment, or even just rig up something yourself (since you're not really concerned with measuring the actual loss, or comparing before/after numbers, just finding the leaks).

Basically, you shut all the doors/windows in your house, and then seal up one door with a big fan blowing out, and then turn it on. You'll be able to clearly feel any drafts where there are openings in your house.



Once you identify leakage, you can determine the best way to seal it up. Caulk and expanding foam are two very good options, and weather stripping for windows and doors can work well. 

Some common sources of leaks:


windows/doors
electrical outlets (in exterior walls)
vents
attic entrances
openings for pipes and wires.


Another benefit, aside from sealing out bugs, this will also increase the energy efficiency of your home and reduce your heating/cooling costs.