Serverless computing is a cloud execution model where developers run code and the server management is handled by the cloud provider. Serverless computing is increasingly gaining popularity as more systems adopt it to enhance scalability and reduce operational costs. While it has numerous benefits, it also embodies unique challenges inherent to serverless computing. One such challenge is Technical Debt (TD), which is exacerbated by the complexities of the serverless paradigm. While prior work has investigated the activities and bad practices that lead to TD in serverless computing, there remains a gap in understanding how TD manifests, the challenges it poses, and the solutions proposed to address TD issues in serverless systems. This study aims to investigate TD in the serverless context using Stack Overflow (SO) as a knowledge base. We collected 78,867 serverless questions on SO and labeled them as TD or non-TD using deep learning. We further conducted a deeper exploration to identify types of TD in serverless settings, issues and proposed solutions, and also explored TD in the code snippets. We found that 37% of serverless questions on SO are TD-related, and that the majority of code snippets contained code smells and security vulnerabilities. We also identified six serverless-specific issues. Our research highlights the need for tools that can effectively detect TD in serverless applications.