There's an invisible 1-Up in the first level of each world, but whether or not it appears depends on whether or not you collected all the coins in the previous world's 3rd level. For instance, in World 3-1, to make the invisible 1-up that's on the bridge appear, you need to collect all the coins in World 2-3.

There are only two exceptions to this rule: World 1-1 because it's the very first level in the game, and World 2-1 where you're allowed to miss 2 coins in World 1-3. However, the hidden 1-Ups will always appear if you use a Warp Zone or the level select trick after beating the game. Another caveat is that each hidden 1-Up will only appear once so if you make the hidden 1-Up appear and lose a life, it won't reappear.