Basing a video game on a movie that itself was based on a comic that was written in the 1900s seems like an odd thing to do, but Little Nemo The Dream Master is just that, apparently.
The game's stages are actually a little on the long side, but you have a secret weapon at your disposal.
Go to the title screen
And press
Up, Select, Left, Right, A, A, B
Done right you'll have a new option, "Dream Select".
If you move your cursor down to it, you can press the A button to hear a sound, every time you do, you'll skip that level. Press it once to start on Level 2, twice for Level 3, and so on.
Which is an easy way to continue more or less where you left off if you decide to give up and turn your NES off for a while.