Thanks for the attention, everyone.
No luck so far.
By the way, both the Mac, laptop and Mini, are running MacOS 10.5.6.
I meant to have said, the laptop is an iBook -- specifically, a 1.33 GHz PowerPC G4 ... but anyway, it syncs okay. I think the problem is between the iPhone and the Mini. Some of the suspects mentioned -- the firewall settings, some kind of password mixup, a local network misfire (wireless routers out the ying yang up in this joint) -- do sound plausible.
I did try syncing the laptop and the desktop computers and then syncing the iPhone right away. No dice.
For what it's worth, here are screenshots of what the iPhone shows me. The app does not quit -- it just stops trying to sync and shows an exclamation point in the middle of the little "sync" circular arrow icon at the bottom of the screen.
http://straightclaw.com/iSyncNot/IMG_0003.PNG
http://straightclaw.com/iSyncNot/IMG_0002.PNG
OmniFocus is generally working well for me aside from this. I can probably rock GTD when not at my desk with just a 5x8 pad of paper and an ink pen and tearing out sheets later and sticking them in a physical in box on my actual analog desk (made of an old door) and then processing that routinely. It's really about capturing and organizing. OmniFocus also nicely prints out little lists for the grocery store, hardware store, trips like that, as far as "doing". So ... later maybe for this iPhone extravaganza. I mean, it is still a kick ass phone, has Pandora, shows me the weather, keeps me from getting lost, takes nice pictures ... I love it.
I do think I will get WebDAV set up and sync everything to that (someday/maybe). Then all this local net confusion, firewall settings, etc., may not matter any more. From what I hear, that seems to work well for people. Then at that point try rocking OF on the iPhone again. But meanwhile I do have actual work that is flagged like "get this done if you want to get paid, my home dog," so ... train keeps a rollin.
Take er easy, dudes & dudesses. :)