Part of making a game feature interesting is making sure that there are a sufficient number of places and situations where the game feature is useful and/or necessary. In the example of the Map in Phantom Hourglass, this means creating puzzles that require the use of the note-taking feature. If done poorly, this could make challenges seem artificial, which can hurt the game experience. However, the map feature in Phantom Hourglass rarely seems artificial in its use. The designers didn't really need to create too many unusual challenges to make use of it. Part of this is that most Zelda games and RPGs in general already present the kinds of challenges that require note-taking.
Common examples so far of puzzles that require note-taking in Phantom Hourglass include puzzles where the order you hit switches is important, puzzles where you need to walk specific paths through areas, puzzles where you need to connect lines between geographic objects, and puzzles where you track the number or placement of objects in an area. However, these puzzles don't feel unnatural, mostly because they are similar to puzzles in other RPGs. Since the player usually has to memorize these things or take notes on pieces of real paper anyways, the addition of a note-taking feature directly into the game is very positive.
Since Zelda games are an open-world exploration games that require a lot of back-tracking, being able to make notes of chest locations and spots where you need new tools saves a lot of time and energy re-exploring old areas. One way Phantom Hourglass takes advantage of that is by keeping many things non-random in their locations. For example, whirlwinds, pirates, sea monsters, and such are all consistent in their locations on the ocean. This gives a definite advantage to mapping out their locations. If the locations of these things were random, the map would be useless.
One of my favorite examples of a puzzle that takes advantage of the Phantom Hourglass map is the Uncharted Island, where the player has to map out the outline of the island to solve the island's central riddle. It was fun exploring the island, charting it out, and slowly watching the island's distinctive shape become clear.
The place where the map is certainly the most useful is in the much reviled Ocean King's Temple. Because the payer has to go through the Temple many times with a time limit, mapping out efficient routes and taking notes on hazards helps a lot with subsequent go-throughs. Taking notes on the locations of the Phantoms and their routes, red pots, gold pots, crystals, force gems, bomb-able paths, and switches can save a lot of effort later in the game. However, the game designers may have gone overboard in stuffing all of this into one mega-dungeon. Creating multiple, somewhat smaller dungeons that the player has to return to multiple times may have been better. However, the dungeon does demonstrate that these notes are most useful during stealth gameplay. I would love to see this kind of map feature in a Metal Gear game.
My one critique of the map is that it can be very hard to make legible notes with the DS stylus that are reasonably small. I usually use lots of small symbols, and even those can be hard to read if I try to pack too many into a small space (which is often necessary in the Temple of the Ocean King). It would have been nice to be able to drag and drop pre-made symbols onto the map for such purposes, or even to be able to make customized map symbols.