Possibly a new bug
I discovered this entirely by accident while working on a ROM hack, but confirmed that it's present in the base game. Doesn't hurt anything, and doesn't seem like it could be potentially useful, but I couldn't find anything about it when I looked it up, got a little excited, and wanted to share.
When playing on a Super Gameboy, save your game in Rock Tunnel (or any dark area, if you're on a ROM hack that has other dark areas) without using Flash. Reload your game, and when you get to the point where you can select Continue or New Game, go back to the title screen, then forward again to the menu. The game will load the third color from three different color palettes (the two logo color palettes and the color palette for Mew) and display them on portions of the screen, then color the whole screen with the color from Mew's palette. At this point, you can continue or start a new game, and the colors clear. It seems to be caused by the game loading in a save where the palette offset variable that makes Rock Tunnel dark has been set.
If you do this on a regular Gameboy (and probably a Gameboy Color) instead of loading three colors, the entire screen will get tinted gray, but once again you can still continue or start a new game without any trouble and the gray will clear up.