Well, the chair back, before bending and extruding, is not perfectly flat. You can flatten it by rotating it so it is aligned with the z axis in side view and the x axis in top view, then selecting all the verts and doing Scale>>Y>>Zero (S,y,0). Make sure the pivot point is set to median point before you do this. This will move all the verts along the y axis to a common plane.
Then you can bend the chair back with proportional editing and extrude a bit of depth to it without getting those nasty artifacts.
It looks like you may have some interior polygons in those trouble spots. Go to Edit Mode, turn on Face Select and turn off Limit Selection to Visible. Zoom in close on those areas where the chair back looks “funky” and see if you can spot any polygons inside the mesh. If you do, delete them. Then Recalculate Normals just to be sure.
One solution is making a bunch of vertical slices through the geometry before bending. Yes it does add a lot more geometry, but the final result is what counts. Without the slices, the geometry will be forced too far out of planar and cause the artifacts you are seeing. This process will work on text as well.
I am having trouble with that myself. The wiki says closing a 2d curve produces a renderable surface, but that does not seem to be happening on my system. Anyway, if you have the surface, you can modify the bezier circles by changing the control handles to “free” (Edit mode, Curve>>Control Points>>Set Handle Type>>Free) then you can make whatever shape you want by moving the end points around.
Once you get the shape, you can convert the bezier to mesh in object mode (Object>>Convert to>>Mesh from Curve). Of couse, if you don’t have that renderable surface, you’ll probably only get vertices for your mesh rather than faces.