iPhone4, the buttons are really too small to click and only a few of them work. You don't need arrows for a touch device anyway. The instruction action looks like it opens a shadowbox but the content inside is too large.
As for browser detection, krpano js already does this.
It wouldn't take much to optimize the tour for idevices.
What iPhone are you using? (3G, 4 or 4s)
I have a 3G iPod touch and it will run, though barely. At some point, you have to build for the trend line. In the US and Canada, mobile devices account for 20% of all internet traffic. A quarter of that is by much more capable tablets like the iPad. I don't know what portion of that remaining 15% is older iPhones, but it won't be increasing. iPhone 4s is now the top seller for Apple. Basically, if I designed a version of a virtual tour like this for such a small and eventually replaced niche, I'd go broke. It's too much effort for a small and decreasing audience.
I've recommended that the Smithsonian employ browser detection to serve incapable devices individual panoramas instead of the VT, but they got excited and posted it as is. I'll talk to them again on Tuesday about a redirect or at least a caveat.
If you get a chance, try it on a nice phone or tablet. It's pretty cool.