When ever you are trying to maintain a lawn there are usually two or thee types of trouble spots you will have to deal with . There is never any one right solution for any of these problems but here are some suggestions that will help.
Thin turf from heavy foot traffic: This may be corrected by the use of concrete stepping stones in heavily traveled areas. If the damage is caused by play then the turf may need to be over seeded on a regular basis to help increase the number of plants and replace those that have been destroyed. You may also rotate the areas allowed for play so that the damaged is minimizes and a new area put to use to allow recovery time for the turf.
Water logged or standing water: Some areas of the lawn may be wet all the time or at least a good portion of the time this could be due to several factors. Maybe it is a low spot that receives run off from other areas. It is also possible that there is a barrier below the surface preventing the water to percolate through the soil. By using drain tile and redirecting and dispersing the water to other areas it may eliminate this problem. It may require in some severe cases the regarding of the area and even creation of a retention area depending on just how much water is involved.
Heavy shade and bare dirt: The biggest complaint from homeowners that try to establish a nice lawn is that the grass will just not grow under trees or along the north side of the building . The grass is too thin in the shady spots. This is due to a lack of light even shade grasses need a certain intensity of light in order to maintain healthy vigorous growth. If the light is insufficient the turf will not grow. Several solutions can be found for this problem.
Thin trees and bushes by trimming back to allow more light to reach the ground. If this is not possible or impractical consider the use of shade loving ground covers or plantings in theses areas. They will help increase the value of the landscape while cutting down on maintenance as well. Maybe the area could be transformed into a patio area using pavers or flagstone. If a patio is impractical then maybe a mulch or even placing rock to create a dry creek bed effect would work. Place the stones along the area to resemble a creek running from top to bottom. You can even build up the sides a little an do plantings along the edge just like a real creek bed would have.
The use of a little imagination may just be the answer for your hard to grow areas.