Ben,
I agree that the Urey-Miller experiment was cool and yes, over time it has been thoroughly questioned. They managed to create 13 of the 22 amino acids that are used to build proteins. I'm not sure what the creationists have had to say about the initial experiment but more recent experiments have shown that amino acids, hydroxyacids, purines and pyrimidines can all be created in these ‘test-tube’ conditions.
Major objections to the initial experiment centred on the amount or composition of molecules within the atmosphere, the destruction of certain molecules by Ultra Violet radiation and the reduction of molecules by oxygen.
As far as I am aware, the current consensus is that the Urey-Miller experiments were pretty valid, they have been run repeatedly with different molecules (based on different calculations on the composition of the prebiotic atmosphere) and under different conditions.
Therefore, I would say that:
1) Yes, the experiment (and more recent ones) are important,
2) Yes, the question does matter. Where life come from is a big topic for biologists.
3) Yes, there have been more recent experiments (a quick search on Google Scholar lead me to Springer Link, where you can register to read articles http://www.springerlink.com/home/main.mpx), search their pages.
4) Why do some argue against it? This is a much trickier question. First is that scientists want to be as accurate as possible and new theories or interpretations of results or experiments further scientific research. On the other hand, if you are talking to creationists who question the validity of the experiments, they are likely to have a different agenda than the pursuit of rigorous scientific research. The creation of basic amino acids is a start on the road to life, it is not the creation of life per se.
Finally, can you argue against people that say it doesn't prove anything? Yes, but you will need a firm grasp of the initial experiment and subsequent work. Further research is required, I’m afraid there is no easy answer for this one!
Dave.