Lime trees in pots can encounter issues such as over or under-watering, nutrient deficiencies, pests, and diseases. Some common pests include spider mites, aphids, scale insects, and citrus leaf miners, while diseases may involve fungal infections like anthracnose or bacterial canker. To prevent these problems, maintain proper watering, ensure adequate nutrients, and take appropriate pest control measures. Consult the lime tree care for specific solutions to these common issues.