Am written already 2 articles in which I explain the problems I encountered with the use of the Home button of the iPhone 4 terminal. I was talking about a wrong interpretation of my actions when I press the button, i.e. instead of a double tap it acts as a single tap and vice versa, etc. I had this problem on iOS 4.1/4.2.1, both with jailbreak, but on iOS 4.3 beta 1 the problem does not appear with the same frequency. It is true that sometimes the button does not actuate the commands exactly as I would like, but these cases are much rarer since I installed iOS 4.3 beta 1 on the terminal.
I don't know if it has to do with the lack of jailbreak or changes to the operating system, it is certain that the button works much better than before. I wouldn't want you to get false hopes about solving this problem, if you have it, but for me the results were positive after installing iOS 4.3 beta 1 and I hope it will be for you too after it will be officially released in iTunes.
