The crown of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is constituted by its spike (S) glycoprotein. S protein mediates the SARS-CoV-2 entry into the host cells. The “fusion core” of the heptad repeat 1 (HR1) on S plays a crucial role in the virus infectivity, as it is part of a key membrane fusion architecture. While SARS-CoV-2 was becoming a global threat, scientists have been accumulating data on the virus at an impressive pace, both in terms of genomic sequences and of three-dimensional structures. On 15 February 2021, from the SARS-CoV-2 genomic sequences in the GISAID resource, we collected 415,673 complete S protein sequences and identified all the mutations occurring in the HR1 fusion core. This is a 21-residue segment, which, in the post-fusion conformation of the protein, gives many strong interactions with the heptad repeat 2, bringing viral and cellular membranes in proximity for fusion. We investigated the frequency and structural effect of novel mutations accumulated over time in such a crucial region for the virus infectivity. Three mutations were quite frequent, occurring in over 0.1% of the total sequences. These were S929T, D936Y, and S949F, all in the N-terminal half of the HR1 fusion core segment and particularly spread in Europe and USA. The most frequent of them, D936Y, was present in 17% of sequences from Finland and 12% of sequences from Sweden. In the post-fusion conformation of the unmutated S protein, D936 is involved in an inter-monomer salt bridge with R1185. We investigated the effect of the D936Y mutation on the pre-fusion and post-fusion state of the protein by using molecular dynamics, showing how it especially affects the latter one.