Spoiler Warning

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Like the Death Star(s), Starkiller base must be mobile. If it needs stars to power up, if it "eats" a whole star in one go as apposed to peeling off layers and a certain amount of stellar mass - which would lead to stellar destabilization and another group of questions - it has to able to move in order to have another star to reload.

If it is mobile, especially if it has a hyperdrive, then it's atmosphere is anything from deformed and heated with frictional on the surface to outright sheared off. Unless this multiple world destroying machine has shields, anti-inertia fields, to protect what is basically the decorative shrubby on it's outer surface.

And since it eats stars, the literal center of mass and base anchor of a star system, then doesn't it devastate two star system? The one which it takes out multiple planets in, the planets in several systems, then the system it fired from, if it had planets, with cooling worlds spinning outwards in any direction. Likewise when Starkiller base is destroyed and a sun is re-created, well off center of where another one was, there should be massive secondary destructive effects. Like planets just freed of one removed star's gravity reeling anew from the reapplied effect that is further off the original's.   
  
Rey's use of the Jedi mind trick was done either to remove urgency from her being in need of saving, make her not be a damsel in distress, or excuse to have Daniel Craig in the scene since he was supposedly the Storm-trooper. Her cell could have just as soon as been empty and her first use of the Force could have been a first absent, more direct once becoming aware it was her, use of simple telekinesis rather than what's suppose to be a more advanced skill. Similarly her "Mary-Sue" status could have been fixed with some indication that she was unconsciously doing Jedi training with her introduction. That whoever left her used the trauma to mentally instill certain habits she repeated daily, then contact with a Jedi artifact - Anakin's/Vader's/Luke's lightsaber - along with Ren's probing and breaking routine "awoke" the Force in her.

Second to last point of contention/consideration: what was Rey and Leia's first ever seeing each other could have been two force sensitive people consoling one another at the lost of someone they both cared deeply for, or the recognition of two long separated family members who may have decided to keep such a relationship formally unannounced. Which is what Abrams was likely aiming for.

And lastly: Though never watched Lost, could never sit through what few episodes I did manage to catch, still couldn't help but notice that Abrams included/inserted an island into the movie. That irks me for some reason.