The all-pervasiveness and dynamic nature of the COVID-19 pandemic warrants comprehensive and constant surveillance of the numerous mutations that are accumulating in global SARS-CoV-2 genomes and contributing to the microevoution of the various lineages of the novel coronavirus. This would help us gain insights into the evolving pathogenicity of the virus, and thereby improvise our control and therapeutic strategies. This study explores the genome-wide frequency, gene-wise distribution, and molecular nature, of the large repertoire of point mutations detected across the global dataset of 3,608 SARS-CoV-2 RNA-genomes short-listed from a total 5,485 whole genome sequences deposited in GenBank till 4 June 2020 using a download filter that eliminated all incomplete/gapped sequences. Phylogenomic analysis involving all existing SARS-CoV-2 lineages, represented by 3,740 whole genome sequences from human-source (out of a total of 63,894 sequences stored in the GISAID repository, as on 15 July, 2020), illustrated that the two major-lineages of the virus contributed almost equivalently to the pandemic. However, entities belonging to the early lineages are still mostly spread over Asian countries, whereas those affiliated to recently-derived lineages have a relatively more global distribution. Mutation frequency in the SARS-CoV-2 pan genome was found to be 2.27 × 10^-5 nucleotide positions mutated per nucleotide analyzed. An overwhelming majority (count: 1797) of the total 2452 instances of single nucleotide substitution detected (in the SARS-CoV-2 pan genome) were found to be transition mutations with cytidine to uridine (CàU) as the most ubiquitous molecular-type (count: 987). Of the 655 instances of transversion detected, the guanosine to uridine (GàU) variant was most widespread (count: 367). All transcribed and untranscribed loci of the pan genome were found to contain mutation(s). nsp3, and S, N and orf3a, were the most point-mutation-ridden non-structural and structural protein-coding genes, respectively, with 435, 300, 171 and 128 total mutations; 349/86, 192/108, 107/64 and 76/52 transitions/transversions; and 189/48, 106/55, 59/42 and 43/31 CàU/GàU substitutions respectively. Potential mechanistic backgrounds were envisaged for the molecular bias of mutations observed in SARS-CoV-2.