When in doubt, try hitting ACTION in strange places. Most of the time, the game will only let you use an item when and where you need it. So try using all your items on random places. And try hitting ACTION on anything you could climb or swing on.
Swinging on ropes/vines in Steppenwolf is a pain. Except for the cage in 5-3, in order to swing on something, you have to hit the arrow key in the opposite direction. If you're trying to swing across to the right, hit the left key repeatedly to get momentum, and vice versa.
If you don't know where to go, take a closer look at your surroundings. Most objects you can move - most of them, anyway - are on a layer on top of the background, and are usually higher quality than their surroundings. Occasionally, though, they'll be buried beneath the "background" - if nothing stands out, try opening boxes or rummaging through bushes.
If you don't need your GTS or it's not working, go into the inventory and shut it off; that's a corner of the screen that's blocked from your view.