Adverbial and adjectival phrases

In high school in the 1950s, I learned that "due to" begins an adjectival phrase, not an adverbial phrase. Thus, "The delay is due to circumstances beyond our control" is correct, but "Due to circumstances beyond our control, the game is delayed" is incorrect. 

I can see that few people observe this distinction anymore, but I nearly fell out of my chair the day I heard stock guru Jim Cramer mention it in passing.

A common misuse of an adverbial phrase occurs in sentences that start with "Firstly . . ." or "More importantly . . .." First, let me point out that "firstly" would be incorrect at the start of this sentence. More important, "more importantly" would be wrong at the start of this one.