Now that the thread has been bumped and I've had a dimension bass for (what, like a year?) a year, I want to update my answer. Speaking as a guy who isn't a trying to get the classic J sound, the classic Stingray sound, or the classic P sound (I have all of those thanks), my double-H American Dimension is the best thing since sliced bread. Solid bottom end to make any country song weep, mid-forward tone to mix with any modern rock sound, and it's the only bass I've owned that will actually deliver a fairly competent J and P sound with a little bit of EQ tweaking.
What's actually wrong with my Dimension bass:
1) the neck pocket has some overspray in it, and needed a paper shim to get the strings back on center. sanding would also have worked, but I didn't.
2) The pots are flimsy. The midrange pot turns all the way around
3) The action barely adjusts low enough. I have the neck adjusted basically flat and the G string bottomed out. You need to mod the bridge or replace it to get a really low action. No I'm not shimming the neck, it's a five-bolt with near infinite sustain, there's no excuse for this.
4) The truss rod is too weak and the neck has too much relief when unloaded. I to tighten the truss rod to the point where I'm a little worried, just to straighten the neck *before* the strings are on. The neck is made of the stiffest piece of wood I've ever seen. So, yes, I'm complaining that the neck is such good quality that the truss rod can't bend it and that's a flaw.
5) The truss rod is double-action. This would be a *great* feature except that it's also kind of hard to turn and needs to be lubed already, and of course for #4. I have to sit on the neck to release the tension to get it to turn. And you can't lube a double-action truss rod so I guess I'll just use it till it breaks. (But the wood is so good it's worth fixing, it's just why should it need fixing at all?)
Yeah, it has design and manufacturing flaws. But as a player, it's a near-perfect design and maybe someday I'll get a second one.