Extensive research is dedicated to understanding if sporadic and familial papillary thyroid carcinoma are distinct biological entities. We have previously demonstrated that familial papillary thyroid cancer (fPTC) cells exhibit short relative telomere length (RTL) in both blood and tissues and that these features may be associated with chromosome instability. Here, we investigated the frequency of HER2 (Human Epidermal Growth Factor Receptor 2) amplification, and other recently reported genetic alterations in sporadic PTC (sPTC) and fPTC, and assessed correlations with RTL and BRAF mutational status. We analyzed HER2 gene amplification and the integrity of ALK, ETV6, RET, and BRAF genes by fluorescence in situ hybridization in isolated nuclei and paraffin-embedded formalin-fixed sections of 13 fPTC and 18 sPTC patients. We analyzed BRAFV600E mutation and RTL by qRT-PCR. Significant HER2 amplification (p = 0.0076), which was restricted to scattered groups of cells, was found in fPTC samples. HER2 amplification in fPTCs was invariably associated with BRAFV600E mutation. RTL was shorter in fPTCs than sPTCs (p < 0.001). No rearrangements of other tested genes were observed. These findings suggest that the association of HER2 amplification with BRAFV600E mutation and telomere shortening may represent a marker of tumor aggressiveness, and, in refractory thyroid cancer, may warrant exploration as a site for targeted therapy.