Basement water seepage can be an ongoing issue that sometimes becomes just a fact of spring. Water from saturated ground can find it's way in through just about any crack or seam in a basement floor and foundation. Sometimes it can even soak directly through solid concrete. If rising ground water becomes trapped, it can build "Hydro-static" pressure, resulting in cracking and heaving.
There are some quick fixes offered from various sources. There are concrete sealants or channels you can glue on the floor. You can install sump holes where ever puddles accumulate, which by themselves work as little more than floor drains. None of these methods are practical or stand up over time. The most reliable, widely accepted and perminent solution is an Interior Drain Tile System.
Radon levels can be a serious concern. According to the EPA, radon exposure is second only to smoking for lung cancer risk. Radon originates from deep uranium deposits. When its inhaled it releases Alpha, Beta and Gamma radiation directly into your lungs. It's similiar to receiving chest x-rays. There is no safe level of radon. What ever your radon level is, you want it to be lower. Radon levels tend to be highest in the basement. However, levels can be elevated on the main floor as well.
In most cases a radon mitigation system can be installed quickly and at a reasonable cost ($1300-$1500). Not only will a good mitigation system reduce radon levels, but it can reduce water vapor intrusion possibly eliminating the need for dehumidifiers. It may lower other soil gasses as well, such as: methane, hyrocarbons and other contaminates. According the the EPA, the most effective Radon Mitigation method is Sub-Slab Depressurization.