stumbling

Romans 14

I read this passage while I was at Identity in Medicine Hat. The key words in the passage are: look down, pass judgement, condemn. The other key idea is that none of us live and die to ourselves but we live and die to God (and, it is implied, to each other).
Paul is saying that we have to give freedom and grace when it comes to certain issues. I was going to say, "when it comes to disputable matters" but the problem is that some people don't think that these issues should be disputable, choosing to make them markers of spiritual maturity and holiness. The issues that Paul specifically addresses here are: eating meat (specifically adhering to the kosher diet), drinking wine and holding certain days as more sacred. Paul says that we must be fully convinced in our own conscience (otherwise we are not participating out of faith and it is sin), that we must not condemn or look down on those who think differently than we do and that we must not do anything to cause someone to stumble.
For me, that last one is what is causing me questions. What does it mean to stumble? If they are offended, have they stumbled? I believe that it means that I must not lead them to sin in that area. I think, from the context, that is what Paul is saying because he ends by saying that if someone has doubt about drinking or eating being right, they shouldn't drink or eat meat. So, if I am thinking this through properly, I believe that Paul is saying that some people will view drinking as wrong and that we must not put them in a position where they might drink against their conscience because that would cause them to sin.