There are many ways to stage this play successfully, but only three to surely do it wrong:
Parody. I like "Into the Woods" a great deal, but my work is not a comedy. To play it for laughs is to betray the spirit in which I conceived and wrote this piece. In fact, it's more like a combination of fantasy, horror, and erotica.
Taking it literally. When characters "fly" or "transform" or "disappear," it's more a suggestion about the quality of movement than anything else. This is merely the most efficient means to do so. Not to mention, it captures the tone and mood of the piece more effectively.
Disneyfication. This piece is emphatically not entertainment for the whole family. Bleaching out the sex, violence, and witchcraft would also undermine much of its power.
With those three hurdles out of the way, pretty much any interpretation is valid. This work deliberately gives a lot of room for the particular aesthetic elements. They are not tied to a particular time and place (in other words, not pseudo-medieval Europe by default). Each time I read it, I can imagine the same events staged in different ways. I hope you can too.