Yes, this is a good test for groups, and just like ANOVA or kruskal wallis, you would follow up these tests with a post hoc test that let's you compare specific pairs of groups to find out which ones are causing the low p-value.
Unfortunately, I'm not sure if qiime 1 has any post hoc tests for anosim. One workaround would be to filter your samples to just have two groups at a time, then run anosim on each of these groups. It's not elegant, but it should work.
If qiime does include post hoc tests, I would like to learn more about them.
Colin