At the start of Up Town's last stage, there are items hidden behind most of the pillars you'll walk behind -the second image above has been taken when some sprite layers have been taken off, so you can see what kind of position the items are in.

There is a extra credits sequence in Final Fight, but I'm not exactly sure on what the exact requirements are to view it. Most places list that you need to complete the game on one credit, which sounds right, however one time me and Ragey were playing through the game, using countless credits, yet we still got the extra credits sequence. Maybe you can view it if you have a really high score?