EDIT: Does the free version of SuSolid with free version of SketchUp do this?

Strange,I have checked it with the latest version of Slic3r and is slicing totally ok for me without complaining.
And also the g-code viewer is showing the properly formed path.

An old video of mine:

It takes me 5 minutes to prepare the model for the genuine STL file.
I did it with Susolid plugin.
The most important is to scale the model 1:1000 and then export the STL file in meters,but don't worry,Slic3r will see it in mm.
Please check if all ok in Slic3r,because I did't check it.

I also use the SketchUp team's STL exporter, as wel ass one that does STL and DFX or something like that. Both have the same problems

Maybe I'll just have to suck it up and use OpenSCAD. I love the concept of it, but in reality making complex shapes can be a large code mess. Trying to juggle in my head a whole bunch of shapes being added and subtracted from each other is a pain, and I would likely make every part in a different file so I'd never get to see them "assembled" before printing to check for obvious math errors.

If anyone knows a good way to convert skp files to STL with very good reliability, I (and many others) would greatly appreciate it!

I'm using version 2013, and can see you're on version 2014.  I don't know if that's part of the problem, but I'll share my experience with you anyway:

I use the "SketchUP STL"  plugin from the SketchUP Team, which is available in the Extension Warehouse.  I'm able to import and export .stl files without difficulty. 

Having said that, SketchUp itself makes some rash geometry assumptions during modeling, that become apparent when exporting for 3D printing.  I attribute this to the fact that SketchUp seems originally intended for 'visual correctness' rather than 'model integrity'; not to the .stl export process.

I use the NetFabb cloud service to good effect.  I find that using 'components' in SketchUp to isolate portions of the model helps keep the geometry sane...often not needing a scrubbing through NetFabb.

Now, I love OpenSCAD and it certainly has its place, but I feel Sketchup would be easier for this project with more geometric shapes and things that I just feel would be harder to describe with math.

The problem I have with Sketchup  is that I finish my model, and it's in a .skp file. Now I've downloaded 2 separate plugins that are for exporting files as STL and BOTH fail to properly export the object. If I export the file and try to slice it with Slic3r, I get almost a non-existant object. Slic3r just freaks and generates almost nothing. Now, if I run it through NetFabb (like I was for a while without problem), the geometry is usually skewed in some weird way. Sometimes round holes are semi-circle holes, and sometimes square channels are triangular channels. I just can't make heads or tails of it.

SO - Is there a reliable way (using an older version of Sketchup/Slic3r, different addons, etc) to make Sketchup export proper STL files that will work in Slic3r? (Ideally with the newest version of Slic3r)

Example skp and stl files attached (*_fixed is after NetFabb  tried to fix it)

EDIT: Just to be clear, I've cleaned up a few files by just completely redoing the entire affected area and it usually works, but I don't feel like having to do this project 3 times over.