My iPhone 4 only shows 256 MB of RAM? I just received my iPhone 4 and Activity Monitor Touch and SYSTEM lite only show 247 MB of hardware memory. But the iPhone 4 is supposed to have 512 MB (of which 503 MB are actually available). I checked with a function of my own (derived from here), too, and it also just shows 256 MB of RAM. I'm running iOS 4.1. I don't believe this is a readout bug as other iPhone 4 owners told me they are shown 503 MB in those apps.

Can anyone confirm this on his own iPhone 4? What should I do? Contact Apple and ask for a replacement device? Or just return the device and buy a new one?
That is pretty bizarre. The iPhone 4 is supposed to have 2x256MB memory modules for a total of 512MB, but it sounds like, for some reason, your phone isn't seeing one of them. Your numbers bear this out too - the iPhone hardware sets aside 9MB of the total memory, resulting in the OS seeing 503MB or, in your case, 247MB.

Definitely take it in and try to exchange it or replace it.