What are the biggest challenges in bioprinting?

Assuming that you are referring to 'printing' mammalian cells; none of the above!

Regardless of the technique used to deposit living mammalian cells (of which there are many), the biggest challenge to bio-printing is the 'ink' – i.e. the physicochemical composition and properties of the extracellular material used as the vehicle to carry and deposit the cells. This material dictates both cell survival (including ability to cope with the stressors of printing - shear, compression, decompression, pH, T°C, osmolarity, light energy, etc.) and subsequent behaviour - proliferation, quiescence, differentiation, death (all forms), transdifferentiation, and ultimately ability to form multicellular tissue.