Extrusion-based additive manufacturing techniques including Direct Ink Writing (DIW) have enabled the fabrication of complex, custom constructs across a wide variety of materials. However, DIW requires self-supporting inks. Embedded Ink Writing (EIW) expands the printable space into less viscous materials, making it particularly useful for soft biomaterials and functional materials. In EIW, a nozzle is submerged into a viscoelastic support bath and extrudes continuous filaments. Because the bath is viscoelastic, it fluidizes at the nozzle, allowing ink deposition, but it behaves like a solid at low shear stresses, holding the printed structure in place. In EIW, filament defects including sharp edges, surface roughness, rupture, and contraction can inhibit shape fidelity and mechanical and functional properties of printed parts. Using computational fluid dynamics simulations in OpenFOAM and in-situ imaging experiments, we determine that these defects can be controlled using the local viscosity ratio, capillary number, and nozzle shape.