In this review, the potential failures and flaws associated with fused deposition modeling (FDM) or fused filament fabrication (FFF) 3D printing technology are highlighted. The focus of this article is on presenting the failures and flaws that are caused by the operational standpoints and which are based on the many years of experience with current and emerging materials and equipment for the 3D printing of polymers and composites using the FDM/FFF method. FDM or FFF 3D printing, which is also known as an additive manufacturing (AM) technique, is a material processing and fabrication method where the raw material, usually in the form of filaments, is added layer-by-layer to create a three-dimensional part from a computer designed model. As expected, there are many advantages in terms of material usage, fabrication time, the complexity of the part, and the ease of use in FDM/FFF, which are extensively discussed in many articles. However, to upgrade the application of this technology from public general usage and prototyping to large-scale production use, as well as to be certain about the integrity of the parts even in a prototype, the quality and structural properties of the products become a big concern. This study provides discussions and insights into the potential factors that can cause the failure of 3D printers when producing a part and presents the type and characteristics of potential flaws that can happen in the produced parts. Common defects posed by FDM printing have been discussed, and common nondestructive detection methods to identify these flaws both in-process and after the process is completed are discussed. The discussions on the failures and flaws in machines provides useful information on troubleshooting the process if they happen, and the review on the failures and flaws in parts helps researchers and operators learn about the causes and effects of the flaws in a practical way.