From Satō Issai 佐藤一斎's 19th-century Genshi shiroku 言志四録 ("Saying what I think: Four records"):

看月観清気也。不在円欠晴翳之間。花看花観生意也。存紅紫香臭之外。

One gazes at the moon to appreciate its purity, not its phase or visibility. One gazes at the flowers to appreciate their vitality, not their color or fragrance.

So, for those keeping score at home, not only are we to look at the moon, not the finger, we must also avoid paying too much attention to whether the moon is full, obscured by clouds, etc.

Or, put a bit less facetiously, Satō is directing us to look beyond outer forms. I do not think it is a coincidence, for example, that this item mentions the moon and flowers specifically — a dyad symbolizing nature as an object of elegant appreciation in the Sinosphere generally ("春江花月夜"), and the subject of Japan's two great "viewing" traditions, hanami and tsukimi.

(Note also that the early history of hanami involved appreciation of plum (ume) blossoms rather than sakura; the specific flower viewed is clearly not the point.)

Update: Should that translation actually be something like "... appreciate its purity, which is not found within its phase or visibility"?