A mint with yellow leaves and dark spots is either suffering from powdery mildew or mint rust. If your mint shows only yellow leaves without black spots, it is likely being over watered or has a nutrient deficiency.
Mint rust gets its name because at the start of the disease, the mint leaves develop orange spots. As the disease progresses, the spots turn black and the leaves start to yellow as they begin to die. Other symptoms of mint rust include distorted, unhealthy growth in the spring and clumps of dead, blackened leaves. To treat mint rust, remove all affected plants down to the roots. Healthy plants should be washed with 111-degree F water and moved to a new location.
Powdery mildew begins as a few gray spots on the leaves. As the disease takes over the mint, the spots darken and the leaves fade as they begin to die. Powdery mildew often appears as black spots from the start of the infestation. The disease is often caused by poor air circulation -- especially in moist or humid areas of the garden. To control powdery mildew, remove infected leaves as soon as you notice the disease. Thinning the plant or moving it to an area with better air flow helps prevent the problem. Watering in the morning when the moisture on the leaves can dry also helps control powdery mildew.
Mints should not be allowed to dry out. Keep the soil moist but not wet or soaking. Over watering washes away nutrients from the shallow roots of mints and leads to chlorosis, a lack of iron that causes leaves to yellow. Improper soil pH also causes chlorosis. With soil too acidic or too alkaline, the plants have trouble bringing iron into their roots. Mints prefer soil around pH 5.5 to 6.5. If your soil is higher than this, mix in peat moss to lower it; if the soil is lower than this, mix in manure to raise the pH. Feed the plants with iron sulfate or iron chelate to replenish their iron.