Usually the lawn will recover with time. Brown spots result from dog's urinating on the lawn. Often the area surrounding the browned out grass will be a darker green. Water the affected areas to dilute the urine content in soil. Severely burned spots may require overseeding to fill in the spots in a lawn.
Moles are very difficult to control.
They forage through your lawn in search of insects and earthworms that they feed on. Mechanical traps are the most effective way to control moles,but require patience and skill to effectively trap. Controlling grubs will not prevent mole damage of lawns. My evergreen shrubs looked fine last fall, but now some have brown leaves. No, in most cases the leaves browned due to winter conditions.