Are you talking about a vinyl liner pool or a concrete pool? The two are very different animals. Vinyl liner pools typically have wall sections of sheet metal and are very flexible so there is really not a concern for detailed geotechnical consideration. The exception of course would be the effect on any adjacent structures, slopes, etc.
Concrete pools by their nature need to be constructed to resist cracking, i.e. leaking. Most notably the walls need to be designed to resist the lateral earth pressures an suitably reinforced to prevent cracking. Bouyancy of the pool is also a potential problem, although usually only if the groundwater table is near or above the bottom of the pool. The provision of a drain in the bottom of the pool can effectively deal with this.
Bearing is not really an issue for either type of pool, assuming it is an inground pool. The weight of soil removed is almost twice the weight of water in the pool so the load on the soil is in effect reduced. Of course if the pool is to be constructed in an area of poor fill, organic soils, etc. then some additional support may be need.