This ible is quite different from my usual. 3D design tips are much more appropriate in video format, and so most of it is in the video. The goal of the video is to show you how to go about fixing a model that has lines and edges that don't connect properly. This being said, the goal of the text part of the ible is to explain a bit more in depth why these kinds of issues arise in sketchup.
Up there is the quick version, at the end you can find the full length, detailed video.
Step 1: Why Sketchup?
So before I even start, if these issues exist, why use sketchup? Well sketchup is great for a few reasons. As far as a mix of simplicity and precision(ish), it can't be beat for the price (FREE!). It allows for very precise and varied measurements, as well as having a wide array of plugins available to make your model work in just about any context.
Step 2: Why Does This Happen?
One of the fun things with sketchup is it pretty intuitively snaps to where you need it to as you build (mid-points, recently of frequently used lengths in the past few steps, nearby corners, points, offset planes etc.) The issue is that sometimes those guesses are slightly off, and even though it looks fine, you can be off by a fraction of a degree or a fraction of a mm.
Now what happens when you are off by a fraction of a mm off line or a fraction of a degree off plane? Well, as you keep building up, all those nice handy features of automatically snapping things eventually snap on to this off-design point, and the errors start compounding. This is even more likely if you use curved shapes.
So why not remove the problematic point\line? ...
Step 3: Why Not Remove the Problematic Point\line?
As you keep building, all of those extra points have been added, and you don't know which part of your model is out of phase or not. Trying to backtrack and find them all and put the new lines in the right place is nearly impossible and quite frankly not worth it. This is why my recommendation is to rebuild parts of, or the entire design.
In the picture above, you can see that I got to a bad midpoint because of software rounding errors when I did it through multiple steps.
Why not just build it in the "reductive" way in the first place?
Step 4: Why Not Just Build It in the "reductive" Way That Fixed It in the Video?
The beauty of 3D modelling like this is that you can solve problems. If the solution was so easy that you could get it on the first try every time, you probably wouldn't be trying to solve that problem in the first place! As you build up, you find unforeseen issues, better ideas. You create, and your creation grows. Don't focus on having it right the first time. Drafts are not meant to be perfect.
So build up, hope for the best, and if you have to, bite the bullet and fix right the first time!
If you want more on the "how to part", please enjoy the full length video.