Integrating JavaScript libraries with TypeScript in Ionic 2 applications can initially pose challenges due to TypeScript's inability to understand additional code, but using Typings can simplify the process by managing type definitions. Typings, which helps TypeScript recognize different JavaScript library types, can source definitions from various repositories such as npm, GitHub, and DefinitelyTyped. A common issue arises when dealing with global definitions, such as the ES6-shim module, which requires specifying its global nature to the TypeScript compiler. Despite initial frustrations, with proper setup, TypeScript projects can seamlessly work with JavaScript libraries, enhancing development efficiency and compatibility.