Additive manufacturing (AM) is a promising technology for the rapid tooling and fabrication of complex geometry components. Among all AM techniques, fused filament fabrication (FFF) is the most widely used technique for polymers. However, the consistency and properties control of the FFF product remains a challenging issue. This study aims to investigate physical changes during the 3D printing of polylactic acid (PLA). The correlations between the porosity, crystallinity and mechanical properties of the printed parts were studied. Moreover, the effects of the build-platform temperature were investigated. The experimental results confirmed the anisotropy of printed objects due to the occurrence of orientation phenomena during the filament deposition and the formation both of ordered and disordered crystalline forms (α and σ, respectively). A heat treatment post-3D printing was proposed as an effective method to improve mechanical properties by optimizing the crystallinity (transforming the σ form into the α one) and overcoming the anisotropy of the 3D printed object.