If you have an example of some markup that causes an error, that would help a lot! If you aren’t sure where it is, try dividing the input file and doing A/B compiles, repeating on the non-functional half, until you’ve got it narrowed down (see Documents ▸ Split ▸ at Selection
).
My bet is that it is really easy to fix, probably with a regular expression, and would illuminate what to avoid in the future, if you wish to continue pairing these tools together (and they can work well together nicely). Some even use it in lieu of an Android Scrivener client, for example.
As for usage, have a look at the user manual project, for some ideas. This is a MultiMarkdown → LaTeX → PDF project, responsible for creating what you can see in the Help menu. The project content in that .scriv itself is old, but the techniques are all much the same.
It’s a good demonstration of blending Markdown and styles, in my opinion. I don’t believe there is one right best answer to which to use—which is part of what makes Scrivener special, and different than just about Markdown authoring environment. It gives you the choice to offload heavy markup to the compiler, demonstrated in this post, but you aren’t locked into working that way, and can use the more powerful or expedient or preferential markup wherever you want.
So, what isn’t shown in that screenshot are the many cases where I use Markdown, because often Markdown very often way more powerful than RTF (or Scrivener’s subset use of it). For example its listing capabilities are far superior, and Scrivener itself has very limited cross-referencing capabilities—it cannot, for example, refer to a figure in the middle of a section in such a way that the reader can click on a link that takes them right to that page.
Most of my projects start out as pure Markdown. I only start adding styles and compile generation if and when it makes sense to abstract something—perhaps to multiple formats. I do this because I generally prefer writing in other tools, like Sublime Text or Vim, using Scrivener more as an outliner and manager. I don’t know about you, but having grown up on powerful text editors, using an RTF-based editor feels like being blindfolded, wading around in asphalt with one hand tied behind your back. It has all of what, four shortcuts for cursor navigation and selection? 
Once you start using styles, plain-text editor integration crumbles. So by that point I want most of the stuff written.