The challenges of visual testing in software development include ensuring a smooth integration of functionality and an appealing user interface, maintaining consistency across different devices, browsers, and operating systems, handling dynamic content loading, browser extensions and plugins, cross-browser compatibility, and responsive design across viewports. To overcome these challenges, developers can use automated visual testing tools, baseline images, parameterize tests, continuous integration, version control for baselines, collaborate across teams, improve performance considerations, and regularly maintain their test suites to ensure a cohesive and visually pleasing user experience on various platforms.