I ran a few tests. The stream I used was:
http://knight.wavestreamer.com:9097/stream/1/If I play the mp3 stream on my Windows 7 laptop using VLC then stream the resulting decoded PCM audio to my Roku using my
SimpleAudioStreamer program to re-encode it and play it on the Roku using SimpleAudioPlayer, then it plays just fine, no artifacts at all.
However if I play the mp3 stream directly on the Roku then I hear the artifacts that you mentioned very noticeably.
So the Roku cannot play the same stream the same way that VLC can play it (and possibly the other players you've tried).
It sounds like there's non-audio bursts of stuff embedded in the mp3 audio stream (possibly the Icecast headers or artwork or something used by the Shoutcast stream). The Roku seems less forgiving of malformed audio than other players.
I'm no audio expert (someone like RokuDale might be able to give a better explanation), but I'd guess there's a problem with the Shoutcast stream, especially considering that you say they already switched streams because of some problems they were having.