We've yet to see anyone else complaining of this issue.
That said, from everything you have said (expect that in your first post you stated that new songs didn't transfer and that they did - that's a bit confusing...), I wonder if you are making your changes while your iPod is connected to iTunes. If so, some changes may not be copied over to the iPod if the Sync has gone past that particular step in the process.
You mentioned about checking boxes so let's make it clear what happens and when: if you have the option to Sync only ticked songs and videos ticked (checked), then any non-ticked (un-checked) song will not be put onto your iPod by a Sync.
I was sceptical about empty playlists transferring to an iPod, but I've just tried it and the one I created did copy onto my iPod Classic. As a caveat that does not conclusively mean that such a list will transfer to every model of iPod - who knows?
You also stated: A newly purchased song will show up in artists but not in the playlist it's dropped in. Are you saying that it does not appear in the Playlist in your iTunes Library? If not, then sort that out first, but don't forget, if it's a Smart Playlist you cannot simply "put songs" into it. If it does appear in the Library version of the playlist, try a further Sync after you have made the change. Does it appear on the iPod now?
The question remains; why does this only happen to you? At the moment, the only thing I can think of is (as stated above) that if you connect your device to your computer and then make changes, don't be surprised if they don't all get copied to your iPod.
