I must be doing it wrong then.
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I just tried your tip and hilarity ensued. Some incorrectly oriented faces reversed, while a bunch of white ones turned gray! 
No need to be annoyed. If there’s a way to select and reverse these areas without drawing more lines, I’d love to hear it, since it would save me some work, and that’s an attractive proposition when you’re as lazy as me.
I’m not annoyed just surprised.
Your hilarity suggests further that there are internal faces in your cylinder.
Honestly, I don’t know why this is happening. I ran purge/fix at the time it was drawn (months ago) and again now. I also ran cleanup3. Close visual inspection of the drawing reveals no indication of anything amiss, such as stray internal faces or the like. These are simple “tubes” or similar constructions, and not anything complex enough to hide sneaky faces or lines or whatever.
Maybe I’ll just redraw these from scratch. If the same problems recur I’ll know I have way bigger problems! 
If you attach the model we might be able to see a problem.
Here’s a part of the drawing which has been candy striping.
tow_cable_shield+anchor.skp (141.2 KB)
(Ignore the plane weirdness of the underside of the lhs construction. It’s just an interface between the walls and the fake weld bead. It’s temporary and also not visible when placed on the rest of the drawing.)
Edit: sumpin’ weird. I just rebooted my laptop and now I can select areas between hidden geometry lines, whereas I couldn’t do that before. Maybe it’s time to run repair on my SUP install…
I suspect the reason you are getting some weird face reversal is because you have intersecting faces in places, this confuses things so sketchup can’t know what is out and in automatically.
This sort of thing causes it. You can see here what I mean.
The same can happen with intersecting cylinders.
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How did you get that segment to be reversed like that? When I open the drawing I sent everything is white. Was it reversed when you opened the drawing? Hmmmm… 
I reversed it to show what happens.
Oh. Phew. I was about ready to toss this laptop into the ocean. 
If the object you are dealing with is a ‘SketchUp Solid’ then turning on ‘Hidden Geometry’ and applying ‘Orient Faces’ on a white face should be enough. Then SketchUp doesn’t get confused by internal faces or openings in the geometry. Pay attention to both @Box’s video’s above.
‘SketchUp Solid’ is what you should be after in the first place.
When I selected a white face and then oriented faces it fixed some gray faces but also created new ones. I thought that was pretty funny, tbh.
Anyhoo, I devoted two days to looking for a quick fix, and then just now I spent five minutes manually reversing the bad faces. Problem solved. And to think I may never have noticed if I didn’t inadvertently delete my materials.
Ok, share that file and point out the offensive object.
It’s kind of huge and complex with a wide scattering of faces involved. Right now I’m trying to figure out how to create those animation videos so I can show you it happening, but it’ll likely take me a month to do it.
Reduce your time invested and delete what is not needed in a copy of your file. I think we are only interested in that single object that isn’t playing nice. Or just copy that object into a new instance of SketchUp and share that file. That is a month v.s. a few minutes at most.
It was this model originally.
While messing around with it I accidentally deleted all the materials. That’s when I noticed the random scattering of gray faces.
Later I wondered how this model would look in Monochrome style, and it turns out much the same. A bunch of reversed faces.
They were spread across multiples parts of the model.
Anyhow, I reversed them all now (I hope), but it’ll be interesting to see if it happens again.
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Is that surpising? Monochrome shows the faces with just the default front and back face colors as if you hadn’t applied any materials. It is the same as if you use Shaded or Shaded with Texture but haven’t got any materials applied to the faces.
What I meant was those are two different models of the same thing, but at different stages of assembly. I was curious to see if both had the same issue with reversed faces.
I somehow can’t see the model. What am I doing wrong.