Your finished quilt will essentially look like a puffy grid. This is easier to see on the back. Chances are you've got a lot of tiny puckers in the fabric and this is okay. It's my opinion that a patchwork quilt should LOOK like it was made at home. All those little puckers give it character!
At this point, if your backing fabric has shifted, or all the layers didn't line up in some way, just trim a little off the edges of the quilt. This happens, and once again, it's okay! (And plus, if you have a tiny little machine like me, or you don't use a walking foot, some shifting is almost guaranteed to occur!)
Also keep in mind that once you wash the quilt the first time the puckers will even out and it will look positively lovely since you didn't prewash the fabrics. :)