Those who have explored the countryside between the bustling city of Greyhawk and the castle ruins of the same name which lie on the hill not a league to the east of the city will testify to the fact that there are a number of strange tunnels and wells about. Wise folks avoid them, for they know that these are but entrances to the fiendish maze of dungeons, pits, labyrinths, crypts, catacombs, and caverns which honeycomb the hill and the rock far beneath it. There are those, however, who eagerly seek these ways, for it is likewise well-known that incalculable treasure also rests within these twisting mazes. Dauntless adventurers sally through these entrances to a hideous underworld, determined to gain great fortunes or die. - Gary Gygax, writing in Wargamer's Digest, June 1975.That quote, part of the introduction to the story "The Magician's Ring", is to my mind both evocative and practical. Later in the story, we are told that at least one of those entrances leads to the lower levels of the dungeons directly. Look for such entrances as I continue my own Castle of the Mad Archmage, naturally, but also consider the practical implications.
By providing a means of entrance and/or exit from the dungeons, even into the lower levels, higher-level adventurers are able to bypass the upper (and, to them, boring) levels and get straight to the action. Such entrances need be nether obvious nor easy to find, making an expedition merely to scout out the terrain surrounding the Castle a possible adventure in and of itself. Also, those using such entrances might not be certain of which level of the dungeons they had entered, unless they explored enough to run into rooms or features which were familiar.
Too many of my own dungeons in the past have been of the "one way in or out" variety. I'm going to take Gygax's description to heart.