Should the entire element on my burner on top of electric stove turn red when turned on?
It might or might not be an issue, depending on what is actually happening and element type.

For "normal" coil elements, if one spot on the element gets red significantly earlier than the rest of the element, it's time to replace the element before it burns out and starts arcing.

A slightly uneven redness is not a problem. As such, pictures would be helpful.