The addition of nano-additives provides a path to improve joint performance. However, it is not clear if the use of these materials can alter the susceptibility of bonded joints to the presence of defects. This work aims to shed some light on this matter, by testing the performance of defective joints bonded with adhesives modified with nano-additives. Two different kinds of carbon-based nano-platelets, including graphene (G) and graphene oxide (GO), were used in this work as additives for adhesives used to bond single lap joints (SLJs). Bulk specimens, as well as three geometrically different SLJs were manufactured and tested. One configuration was manufactured without defects (WO), another with a disbond defect in the middle of the overlap, and another with a disbond defect on the edge of the overlap, known as a side defect (SD). These specimens were bonded with a neat epoxy adhesive and with the same adhesive modified with the addition of 0.3 wt% of G and GO. The addition of G and GO was found to improve Young’s modulus and the strength of the epoxy adhesive, while also decreasing its toughness. Dual effect of G and GO addition on improving the strength of the neat epoxy and WO SLJs while reducing the strength of some defective SLJs is also discussed using FT-IR and Raman spectrometry as well as scanning electron microscope pictures of the fracture surfaces.