Here's a fixed version. Draped it onto a surface to make sure it was flat. The main things wrong were the parallel lines didn't often meet the faceted curve - fixed by copying a long line at the centres drawn multiple times, overlaying existing lines and auto-cutting curve's edges, then deleting unwanted bits (v7 auto cuts intersecting edges). A few unconnected vertices and strange overlaps didn't help. Make Faces was not needed that much once that was fixed... There are still a few messy bits around the circular shape - suggest you might redraw that over the top [in a group], then erase the unwanted mess and then explode group to insert the good circle etc ? Note this version is stripped down - no layers, materials etc... 680_LagoonaTilePattern[fixed].skp

Use a Style where the profiles are heavier than other edges, perhaps with line end markers. To make sure it's all 'flat' use a v.big rectangle below it all and then Drape it onto the rectangle using the Sandbox Tool. It'll form a flat copy below on the face... Move the original stuff out of the way, or hide it etc till you need it no longer. Now any edges that are faced will be thin and the problem ones shown thicker. Try drawing some diagonals between junctions across incomplete [unfaced] areas to roughly triangulate them and you should find that slowly they face and the number of visibly fat edges reduce. Delete the unneeded temp edges as you get a stable face; however, if deleting an edge removes the face(s) there's a problem with the adjoining 'faced' area - undo and retry... Zoom into the edges around any stubborn 'gaps'' in the faces or edges drawn over faces that remain heavy and don't split them - it might be that you have some small gaps or overlapping edges - heal them by drawing new edges or moving line ends so they touch another line. Sometimes overdrawing some edges is the quickest way to fix it - particularly if it's a really rubbish CAD drawing...