As has been said, you've got to regard these things in context. It's pleasant enough but ploddingly tepid and a regular skip for me. However, "Love Me Do" will obviously always occupy a unique niche not just in Beatle lore but in pop history, because it was the first piece of fab four plastic which, at 45 r.p.m., lit the blue touchpaper....
Out of context and judged as a stand alone record it was simplistic and unremarkable, even by the unsophisticated standards of 1962. The gulf between it and the breathtakingly dynamic follow up, "Please Please Me" (which for me will always be one of their greatest recordings ever) was astounding. It was "Please Please Me" which smashed down the gates in the domestic market and announced something wholly new, fresh and vibrant in a way that "Love Me Do" never did. After that of course there was no stopping them.