yeah buggy - old iPhone never had these quirks - text pad freezes halfway in the power down sometimes, and some letters don't want to work for type input - have updated the OS - sometimes all type letters are very stubborn sometimes it is just "t" etc.
You can only buy apple care on a new device. If your phone is still in warranty, go directly to Apple with proof of purchase and get a warranty replacement.
Apple care would extend your warranty for a second year. At the time you get a warranty replacement from Apple, you can ask about buying the extended warranty at that time.
Verizon provides consumers with the option of adding Apple Care upon purchasing a new iPhone as well or by contacting Apple directly. Whether you purchased it from Apple or Verizon it's still the same phone. You can actually purchase Apple Care at ANYTIME within your one-year limited warranty on the iPhone. That's a fact.....
BTW, your phone is not defective and you should definitely just restore it via iTunes as a new iPhone to easily fix the issue if it persists. Solutions: Clear out your RAM by holding down the power key, once the slide to power off option comes up let go and press and hold the home button until it kicks you back out to your home screen. So easy and effective if your phones running sluggish. Also go through a Soft Reset by holding down the power key and home button simultaneously until the Apple logo appears on the screen and then let go, it will restart on it's own.
Thanks for the help!
Have tried the standard fix it steps you described - thank you BTW: cleared RAM, soft reset, and all the updates, it is current.
It's also not a greasy screen.
Also read on other forums this particular phone has this problem, others reporting similar bugs/behavior, and are getting their phone replaced from Apple -- many of these reports also describe additional issue of a grey line, which I don't have, at least yet.
Haven't even had the phone for 4 months yet and this is a recurring buggy issue but I can not get it to behave like this predictably yet.
IF it were me, I would get it replaced.