Following the recent rise in generative artificial intelligence (GenAI) tools, fundamental questions about their wider impacts have started reverberating around various disciplines. To this end, this work was undertaken: (i) firstly, to track the unfolding landscape of general issues surrounding GenAI tools; (ii) secondly, as an exploratory inquiry to elucidate the specific opportunities and limitations of GenAI tools as part of the technology-assisted enhancement of mechanical engineering education and professional practices. As part of the investigation, we conduct and present a brief scientometric analysis of recently published studies to unravel the emerging trend on the subject matter. Further, experimentation was done with selected GenAI tools (Bard, ChatGPT, DALL.E, and 3DGPT) for mechanical engineering-related tasks. The study identified several pedagogical and professional opportunities and guidelines for deploying GenAI tools in mechanical engineering. Besides, the study highlights some pitfalls of GenAI tools for analytical reasoning tasks (e.g., subtle errors in computation involving unit conversions) and sketching/image generation tasks (e.g., poor demonstration of symmetry).