Dave the language guy at Balashon writes about the seasonal greeting Gmar Chatima Tova, approvingly citing Passing Phrase, which translates it as meaning "Literally: A good final sealing".
There's just one problem. The grammar of the phrase doesn't support that translation.
"A final sealing" is "gmar chatima". This is a compound phrase (semikhut for Hebrew grammar mavens), in which the base word is "gmar", meaning "sealing". (Correction - I meant to say: "gmar", meaning "finalization".) The gender of the phrase should therefore be the gender of "gmar", which is masculine. But that would demand a masculine form of the adjective "good", yielding "gmar chatima tov"! (Fast talkers sometimes correctly shorten the phrase to "gmar tov", "a good finalization". Adding "chatima" doesn't change the gender of "tov".)
To maintain grammatical correctness, the phrase should be translated a bit differently, as wishing "A final good sealing". As if the "good sealing" is presumed already to exist, and one is wishing for that to be finalized. This is a plausible interpretation after Yom Kippur, when one's fate has already been sealed. But during the preceding ten days of penitence, it is hard to justify. In any case, it is not the common way the phrase is understood.
Rather, I would stick with the original translation, and assume the phrase is simply grammatically incorrect. As a folk greeting which developed over time, either it was originally formed incorrectly ("gmar chatima tova" just sounds right; "gmar chatima tov" doesn't) or grammarians were simply less pedantic about such details as noun-adjective agreement.
Evidence for this understanding is provided, conveniently, by the common pre-Rosh Hashana greeting: "K'tiva Vachatima Tova", "A good inscription and sealing". Since the noun here is compound, the adjective should be plural: "K'tiva Vachatima Tovot"! The singular form properly translates as wishing "An inscription and a good sealing" - an unlikely interpretation, to say the least.
Perhaps "K'tiva Vachatima Tova" just rolled off the tongue (it rhymes!), and "K'tiva Vachatima Tovot" didn't. Or the phrase began as "K'tiva Tova" and the "Vachatima" was added later, inserted with blatant disregard to grammatical technicalities.
I find this all a bit ironic, since I remember as a youngster being very careful to pronounce the precise greeting specified in the Machzor for each type of recipient: "L'shana Tova Tikatev V'techatem" to a man, "...Tikatevi V'techatemi" to a woman, and so on for plural groups. Today I casually rattle off a holiday greeting which is just grammatically wrong. Oh, well.
However you say it, I wish you a final sealing for good. On Yom Kippur we're sealed, but sometimes God has been known to sneak open the envelope for a last minute adjustment on Hoshana Raba, the last day of Sukkot. Or so I'm told. So we continue to wish a "Gmar Chatima Tova" until then.