Some times the follow me tool creates miters at corners, other times it doesn’t and I can’t find a way to control it. What’s the secret?
Avoid making lines parallel to the axis on the profile to make a miter. As far as I know, follow-me never creates miters when the profile is parallel to the axis.
Parallel profile
Non-parallel profile
Also, sometimes follow-me doesn’t result in smooth edges because the curves are exploded.
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Taking your example, isn’t that just because it is creating a flat plane without junctions? By “mitre”, you must mean a line indicating a joint that would exist in, say, a physical picture frame. Is that what the OP meant too?
Also, being pedantic, by parallel to axis, you mean all lines forming the shape to be extruded, since if you twisted the rectangle so that it was itself not parallel to the axis, it would make no difference. Is that right?
yes that is what I meant. It must have been some geometry that I created and my old brain forgot about as I cannot reproduce the effect.
Is it possible that it’s as forestr showed? If the resulting face is in a plane parallel to the plane of the path, there’s only one face created.
The irony here is that in cabinet making, the aim would normally be to get a joint so fine as to be almost invisible, as if the framed article were hewn out of a single block of wood. Exactly as SU makes it when its a flat plane!
It’s not so much to make it look like it was carved out of a single block of wood. It’s to make strong connections between parts, avoid short grain parts, and make best use of the materials.
Of course in SketchUp you need the miter lines to limit the material so you can properly orient wood grain textures.
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In the case of a frame (as discussed here), yes. But if you were jointing up planks for a table top…
But then that wouldn’t be a miter joint. That would be an long grain joint. If you made a table top of solid wood with a mitered frame and glued it all together, it would destroy itself with seasonal movement. A mitered frame on a table top would be more a decorative thing. The panel would be loose so it can float within the frame.
It would be great if the tool did create the geometry at corners so you could actually copy individual segments and build the edge band so you could use it in a cut list. Adding the lines is a bit tedious but it’s still slightly faster than creating new geometry on every edge. But then the tool wouldn’t be as useful in other applications I guess.
Profile maker?
Profile Builder. 
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Isn’t it just that you get to see these edges with separate, though connecting, edges in a path? Contrary to using ‘Follow Me’ on a curve (say circle, arc or any number of welded edges). Here the geometry is hidden but still exists.
Try ‘Follow Me’ on a square and then do the same thing using it on a four sided circle → compare → see the differences. in the corners.
I was in fact using weld on the path of some of the objects but still can’t reproduce what I thought I saw. I thought maybe I was not aware of some additional function in the tool.
I think you can make miters with convexify.
