A few adventure games with point-and-click user interfaces require the player to click a tiny and inconspicuous area of the screen to advance the story for no particular reason except that that particular pixel is difficult to find. This is lazy design— a cheap way of creating an obstacle for the player without any entertainment value. Indiana Jones and the Holy Grail, for example, requires the player to click exactly on one pixel during the end game in order to duck under a swinging blade. For most players, this is a tedious and irritating solution to a well-known movie sequence.
A backward puzzle is one in which the player finds the solution before finding the puzzle itself. She finds a key but doesn't yet know of any locked doors. However, she picks it up and carries it around with her all the time, just in case. When she does eventually find a locked door, she immediately has the solution, which means it's not much of a puzzle. By including a large number of backward puzzles, you force the player to carry around a big inventory of stuff that she has no idea why she's carrying. It encourages players to pick up everything they see whether they need it or not, which is now considered an outdated mechanic and harmful to the game's immersion. A few backward puzzles are OK; a world full is poor design.
You may run across situations where you didn't intend to insert a backward puzzle in your game, but the player finds the solution before finding the puzzle because it's difficult to predict in what order the player will traverse the terrain of the game. It's not always possible to prevent the player from finding the solution first because the solution has to be available, but it can be inconspicuous—a poster on a wall full of posters or an object in a trash can. Be aware, however, that inconspicuous is not the same as obscure or nonsensical. If the key to a puzzle involves finding a live monkey, the monkey shouldn't turn out to be locked in a freezer.
A FedEx puzzle is one that you solve by picking up an object from one place and taking it to a different place, as if you were a courier. Of course, carrying objects around until you find a place to use them is a common feature of adventure games, but some games consist of little else. This gets dull after a while, especially if the solution to a puzzle consists only of fetching and carrying without any lateral thinking or other activity. Liven up the game with a variety of puzzles and tasks. Create objects that have a variety of different uses, such as Indy's bullwhip in Indiana Jones and the Infernal Machine, or objects that are left over from one puzzle but have a part to play in another.