A couple of things to note.
1. Apple did you a favor by taking back a phone that they did not sell you. They are under no obligation to honour another company's warranty.
2. How they do that is entirely up to them. They met their obligation by replacing a phone. They have no obligation to you to replace the accessories or the box it came in.
3. What would you have them do with the accessories and the box? Can they resell those things after you've opened it?
4. Apple replacements come in a white box. It's been this way for a very long time and it's how they do things. The phones in the white boxes are actually a mix of refurb and new. Whatever you get is dependent on the luck of the draw.
5. Apple refurbs are as good as if not better than new. When Apple refurbs an iPhone they strip it, give it an entirely new shell and replace any parts with new parts if they fail under testing. When they're done with that Apple runs the phone through the same battery of tests as the new phones. You got what you perceive to be a set of bad phones one after the other. Apple makes a gazillion phones at a time and there are always some defects. Which leads to number 6.
6. You should have examined the replacement in store and pointed out your problems to the Genius right then. There would have been no denying it and the Genius would most likely have opened another box until you were satisfied. There are plenty of stories here on MR of people going through 8 or 9 boxes before they finally got what was acceptable to them. You walked out.
I will grant you that Apple has some jerks working for them and that you've been treated poorly customer service wise. But, again Apple chose to help you when they didn't have to. Your problem was with a third party store. You really are at the mercy of Apple's good graces at this point.
5. Cannot be true, or the OP would not be complaining. The phone was not recased.
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If his/her replacement phone had dents in it They didn't do a very good job did they.
I think people have the illusion that Apple recases all the iphones before sending them back as refurbs. This case proves otherwise.
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I feel for your situation.
1. I think you will find most iphones have a loose power button, mine does, but once it goes into a case you do not notice.
2. you have the right to have a product you are happy with.
3. within the 2 weeks you should have got a new one.
4. refurbs are a lottery, do not believe that they are better than new. As you have just learned.
5. its interesting how far you got through the process with exchanging the unit, given its in your mothers name
6. can you get your old unit back? I would get you mum to call carphone warehouse and deal with them to replace the unit.