Consistency: the only case where he used BCE is in an image caption. The description on Wikimedia Commons uses BCE, so my guess is that he defaults to writing BC but reading that subconsciously put him in the frame of mind to write BCE. From a skim, he never uses CE or AD in this article.

Omission: this confused me at first, but really the entire article is set 3000 years ago, so it's not particularly ambiguous. If you think in the context of "lecture on the bronze age" you wouldn't expect him to specify every time.

Lack of consistency seems entirely normal to me for a blog post.

At a certain point the information is simply redundant. The meaning of the naked number can and will easily be inferred from context. You don’t even notice it. Both while writing and also while reading. A proper proof reading will catch that (maybe, though I myself am actually hilariously bad at proof reading and miss obvious stuff all the time, so being able to properly proof read and catch things always seemed like a super power to me) but I don’t think this blog author does that (and I don’t really expect it? It’s fine …)

It totally get that there are people who will be endlessly annoyed by that – I’m also annoyed by people using quotation marks the wrong way. But it doesn’t really impact readability of the context is clear enough (as it obviously is in this case).