Alright let's start of this with a big fat...
Spoilers for Game of Thrones Season 1 - 5 and the first episode of season six. Also, possible spoilers for the rest of season 6.
Let's get started
At the end of the season premiere we saw Melisandre completely underdress, including her necklace. We see that that her necklace appears to keep her youthful. She then goes to bed and the episode ends.
What happens after this? Is she dead? Can she still resurrect Jon Snow? Does she always take off the necklace before going to bed?
Alright, so if Melisandre laid down to embrace death after a long life, this can mean a lot to the story.
We have seen people being brought back by the power of the lord of light. After the initial shock of Jon Snow's death, everyone got real excited when they realized that Melisandre was at the wall and could bring him back. But now she might not be there to save Jon.
If the R+L=J is true, that could possibly mean that Jon Snow is the key to defeating the white walkers, since he might be able to use dragons to burn ice zombies up. Also, since Jon has died (but come back) he is no longer obligated to serve the night's watch. He can go down to King's Landing and warn them that winter is coming. He could join Daenerys and help her become queen (I think Daenerys would do more about the white walkers than Tommen or Cersei).
But why would they tell us that Melisandre is so old if they were just going to disregard it and have her bring Jon back anyway?
When Melisandre takes off the necklace at the end of the season premiere, the stone in it gives off a slight red glow. Does this mean that the magic in it has run out?
This could make for an interresting episode, where they have to get Melisandre (now very old and fragile) to Jon before he turns into a white walker or Melisandre dies herself. And this would preferably happen without the night's watch or Sir Alistair noticing.
But maybe Melisandre does die in her bed? Maybe after seeing Stannis fail to invade Winterfell realizing she had the wrong king and then seeing Jon Snow's corpse she falls into some kind of depression and think she's failed, seeing no purpose anymore.
Everything has a purpose in Game of Thrones
In game of thrones, everything has a purpose. Nothing random happens to main characters. If Melisandre didn't have purpose at the wall she wouldn't have come there. There's a reason she's there and there's a reason we saw that she's old. We can't be sure with anything on Game of Thrones, but there hasn't been a random occurrence thorugh-out the series and something will happen with Melisanre at the wall.
So what do you think will happen next with Melisandre, Jon and Westeros?