I noticed my jade plant had bugs crawling all over in the soil. They look like tiny gnats but I am not sure. It has been losing a lot of leaves and I wonder if this could be the problem?

Jades should be given a thorough watering and then not again until the soil is dry. They also like direct sun, as much as you can give it during the day, but it should be done slowly if your jade is not getting that kind of light now. Low light can cause leaf drop, as well as over-watering and under-watering or any pest on the plant.
As far as the pest in the soil, not sure what you have, you can either change the soil, or, try flushing the soil out several times in secession at watering time, then replace any soil that was lost.