Apple, please resolve this.
Not aimed at you personally, but this isn't the best place to get Apple to notice a problem - and certainly not get them to examine and resolve it. Apple provide this as a user-to-user support resource, so you're really only addressing other users here.
I would urge those who have this issue to call Apple or take your iPhones to an Apple store (whichever is more convenient) to discuss the issue and seek help with it. Not only will that get Apple's direct attention, but also be more likely to get you some credible assistance if other users here have not been able to.
I would have to say that since my iPhone does continue to autocheck, this is not likely to be a problem specifically with the 1.1.1 update, and as such unless reported to them directly, Apple may not even be aware it is happening. For those for whom a resolution to this is still outstanding, the first steps I suspect Apple would suggest you try is at first a reset - done by holding the sleep/wake and home buttons down until the Apple logo appears. This will reset the iPhone, but not cause data loss. It will cause usage meters to revert to '-' until the next full charge is achieved. Next step would be a full restore via connection to iTunes. Beware this will remove user data from the iPhone, requiring it to be re-synced afterwards. This will return the iPhone to out-of-the-box condition (excepting for the 1.1.1 update which will still remain, even if the iPhone was originally supplied with an earlier firmware version.
