Is all pressure to do the right thing bad?: It depends on the right thing. Even on some basic levels on right people wildly disagree. If the pressure was doing something he felt was morally wrong, then it is a bad thing.
Was it wrong for Uncle Ben to tell him that with great power comes great responsibility?: Since Peter took thins to be a personal motto, and not something he makes other people follow, I personally see this as a good thing. It could be taken either proactively of passively. Proactively is of course using it to help people, while passively is doing no harm to other people. Taken as a must help others, I would balk at it. Taken as don't hurt others, and I'm happy with it.
And I was saying yes to "You can choose not to pick something up if it's an option, but if you choose not to pick up a responsibility, you're doing the wrong thing." Only taking "wrong thing," as evil, as opposed to "incorrect choice."