I've seen many "flakey" home buttons be a problem with the software and not a real hardware issue. Getting it into the hands of a Apple Store technician is great as they are trained to work with you to isolate the issue to hardware or software and reach resolution or a plan to isolate it further. I would be prepared to let them erase the device (have a portable or backup made at home before leaving for the store) so they can eliminate software as a cause while you are in the store. That saves both of you a return trip or loss of data/contacts/apps.
Since they see hundreds of devices a week and have no incentive to not swap your phone if it's really a hardware issue, they will often see minor physical things before most end users will.
As to flakey software, oftentimes a physical home button press gets delayed or lost due to the OS doing a task (garbage collection / memory warning) or a runaway process taking lots of CPU.
Here is the procedure I use to be sure it's a bad home button hardware if I'm on the fence taking an iOS device in for service and it's not convenient to simply erase the device and set it up as new to get the cleanest OS setup possible.
- Turn on airplane mode - this
isolates the phone from wifi and
- Do a clean shutdown
with "slide to power off" and the
red slider - then reboot the phone
and don't slide to unlock.
This creates a very minimal system with only the core system running. You can repeatedly alternate the sleep/wake and home buttons. Play around a while - light presses, slow presses, firm presses. Find how little pressure is needed to activate the home button.
If the button is failing - you will get failures in this minimal system. One out of ten or one out of 100 or 50% of the clicks will fail. You will be able to quickly determine a spring failure from a contact failure from any other hardware failure in 10 minutes of testing. You also have a repeatable test case to show/demonstrate the failure and not get to the store with a "ghost" problem that can't easily be reproduced.
If the button isn't failing - you will know it in your bones - the hardware button on the iPhone doesn't just get tired or fail - it's a very simple contact and spring mechanism. When it breaks, the most normal failure mode is total failure.
If it's not failing - then you have a software issue - something is bogging down the system so that the hardware signal is getting delayed. Perhaps a call to AppleCare or a visit to the Genius Bar is also very good for fixing software too.
So to sum up - do get help either way. Your phone should be responsive to home button presses. With a little knowledge, you'll quickly figure if it's one bad app - the phone needing a restore and set up as new - or a hardware repair. I wouldn't restore the phone just before taking it in - that will erase two weeks of error logs that might help point to the problem - but be prepared to let them wipe the device if needed to rule out software.