Is there something wrong with the corn kernels that don't pop? Usually, at the end of a bag of popcorn, or when you pop your own on the stove, there is a certain number of kernels left unpopped. Why is that? 

Is there something that changes in the kernels that makes them different from the others or are they the same, but the heat isn't distributed to them well enough? 

Is there any way to make more of the kernels pop without burning the ones that popped first?
Popcorn kernels pop because moisture is trapped inside of a relatively gas-tight shell. As the kernels are heated, the water inside the kernel turns to steam. The shell of the kernel keeps the steam from expanding, so pressure builds up inside of the kernel until the whole things blows open.

If the kernel doesn't have enough moisture inside of it or if the shell of the kernel is permeable enough to allow the pressure inside the kernel to dissipate before it reaches the critical pop pressure, then that kernel won't pop. Ever.

So to answer your question, no. Take the popcorn off the heat before the popped kernels burn.