One problem that could result is borers. These are insects that feed in the trunks of stressed trees. Gardeners often notice sap or sawdust on the trunks of the affected trees. Regretfully unless it's detected early the trees are often to far gone. You can help trees that are under stress by just giving them good care.
Adequate water is all that is needed by most.
If you are watering the turf and other landscape plantings this is usually adequate. Where needed sprays available at garden centers can be applied to protect the trunks from insects. When trees are affected by drought one of the long term affects is their susceptibility to trunk diseases, often called cankers and root rot organisms. There is no good control for these problems except to give the trees normal care during the stressful times. Again if you are watering your yard to save the turf, flowers and shrubs the trees should be getting all they need at the same time.