How accurate are the species counts?
Counts are accurate to whichever taxonomy you have chosen as your primary one — which is the only way the question has an answer.
Updated
Your species counts are accurate to the primary taxonomy you have chosen. That qualification is not a hedge: two taxonomies genuinely disagree about how many species there are, so a count only means something once you have said which one you are counting by. Bird Journal looks to your primary taxonomy first for names, for counts and for how species are classified.
Taxonomies are also only offered in the countries they are relevant to. That is what stops a count drifting as you travel: without it, the same bird recorded in two countries could end up counted against two different ideas of what it is.
If your counts are not what you expect, the usual cause is a taxonomy update with changes still waiting on you — a split you have not resolved leaves records against species the taxonomy no longer recognises. Taxonomy updates covers how to work through those.