To get the most obvious thing out of the way: this new series plays like something CBS would have shown ten years ago, not like something you'd find on HBO. Since it is nonetheless on HBO, you'd have to think a large chunk of its potential audience will be missing, at least until the inevitable release on home video.
It's a fine series, based on the two-hour opener. Jill Scott is good (I have no idea how good a job she does with her accent ... I didn't hear any Philly, for what that's worth), as is her supporting cast. The mysteries were a hodgepodge of light and dark, but even the darkest lacked any real sense that the heroine was in danger. Which is to say, it's a pleasant show that takes full advantage of its Botswana setting, which turns the most familiar detective shenanigans into something fresh.
I don't watch much that could be called "family television," and as I say, the fact that The No. 1 Ladies' Detective Agency is on HBO will keep it from being in the homes of very many families. But it's one of the rare shows that I can recommend to pretty much anyone reading these words, which couldn't be said for other, better, HBO series like The Wire, Deadwood, Rome, or The Sopranos. B+.