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I hope one of our server-level configuration gurus will stop in and help you out. Things get a bit quiet here over the weekends, so it may be monday before we can get an authoritative answer for this and your other post.
We'll just hope it's not that long, but I wanted to roll out the welcome mat and say hello!
One remote possibility is that the failing browsers have been set to use HTTP 1.0 rather than 1.1 and so do not send the host name (so no way to choose the right one), but I can't reproduce that type of problem with MSIE on Windows.
The actual config looks fine, I use basically the same (with Apache 1.3), works fine. I assume you have a "NameVirtualHost *" line somewhere earlier in the config.