Different magnesium incorporation behavior has been observed in heavily Mg-doped AlGaN epitaxial layers. The films were grown by metal-organic vapor phase epitaxy involving a lateral overgrowth technique on patterned sapphire substrates. TEM observations show that direct growth on sapphire exhibits pyramidal defects, while lateral overgrowth is homogeneous and free of structural defects. The orientation of the growth front significantly influences the microstructure, and the {0001} growth facet appears to be essential for the formation of the pyramidal defects. In addition, cylindrical and funnel-shaped nanopipes have been observed at dislocations with an edge component. The relationship between Mg segregation and these defects is discussed, and formation mechanisms are proposed taking into consideration the orientation of the growth front.