I tried to make a pawn from a reference image with the bézier curve and when I converted it to a mesh object and spun it, there is this unwanted edge running down the middle.
Does anyone know how to fix this?
When you spin 360°, start and end point do not get joined automatically. So what you have are two sets of vertices sitting pretty exactly on top of each other. That won't show with solid shading (without a subsurf), but as you see, with smooth shading, it does.
The left cylinder is clean and you can see the highlighted edges on both sides while the right cylinder shows problems by only having the right half of the edges selected.
The remedy is to select the doubled verts (or all of your mesh if there are no necessary doubles somewhere) and hit W4, remove doubles. All the verts that are closer than the tool's threshold will get merged into one.
On occasion it's also necessary to recalculate the normals by selecting everything and hitting CTRLN.