From Garner's Usage Tip of the Day:
As an introductory phrase, "more important," has historically been considered an elliptical form of "What is more important," and hence the "-ly" form is sometimes thought to be the less desirable. Yet three points militate against this position.
First, if we may begin a sentence "Importantly, the production appeared first off Broadway . . . ," we ought to be able to begin it, "More importantly, . . . ."
Second, the ellipsis does not work with analogous phrases, such as "more notable" and "more interesting." Both of those phrases require an "-ly" adverb -- e.g.: "More interestingly, he earns lots of money." David Beckham, "Why Are They Famous?" Independent, 31 Aug. 1997.
And third, if the position is changed from the beginning of the sentence in any significant way, the usual ellipsis becomes unidiomatic and "-ly" is quite acceptable -- e.g.: "Shrage believes that the strategy should not be to reverse the intermarriage rate, as some activists argue, but to make sure that intermarried couples embrace Judaism and, more importantly, commit to raising their children as Jews." Diego Ribadeneira, "Jewish Community Flourishing, New Report Says," St. Louis Post-Dispatch, 6 Sept. 1997.
The criticism of "more importantly" and "most importantly" has always been rather muted and obscure, and today it has dwindled to something less than muted and obscure. So writers needn't fear any criticism for using the "-ly" forms; if they encounter any, it's easily dismissed as picayunish pedantry.