UI automation testing faces several challenges including lack of awareness of automation tools, limitations of the tools themselves, constant changes to the UI, increasing complexity of products, and issues with error handling and synchronization. Some specific problems encountered are difficulties recognizing tabs, toolbars and child objects, as well as problems with images, colors, and drag and drop functionality. To overcome these challenges, testers must choose the right automation framework, start with effective test design, maintain coding standards, write efficient and reusable code, avoid over-reliance on recording, and thoroughly document tests.