I'm using Vim 8.0 and the default syntax/markdown.vim that comes with it, which is the 2016-08-20 version of Tim Pope's vim-markdown package.
This package has a bug that really annoys me on certain files: it considers any line indended by four or more spaces as a code block, including list continuations. Thus, in the following:
1. Agenda Item 1: Frob the Bazzit
- The bazzit is something that makes us have
very _short_ lines indeed.
- Further frobbing is necessary
The line very _short_ lines indeed will be highlighted as a code block and the word short will not be italicised.
I'm happy with just completely disabling code block highlighting, at least in these circumstances, but I can't figure out how to do that after the fact. I've been testing with a ~/.vim/after/syntax/markdown.vim to tweak configuration, but I can't figure out how, once the
syn region markdownCodeBlock start=" \|\t" end="$" contained
has been executed in the system markdown.vim I can disable that in my after/syntax/markdown.vim. How do I do this?
(I have tried using highlight link markdownCodeBlock NONE, which does disable the code block colour on those lines, but unfortunately they are still marked as code block regions and still do not highlight any other markup in there, such as _italic_ or `code` inline markup.)

I'm happy with just completely disabling code block highlighting, at least in these circumstances- padawinmarkdown.vim(from tpope). Based on that created the following PR: github.com/tpope/vim-markdown/pull/140. To see if it will be accepted or not ¯_(ツ)_/¯ - padawinsyntax clear markdownCodeBlockin my~/.vim/after/(None so far.)syntax/markdown.vimand will see if I find any issues with it. In the meantime, you should expand your comment above and the patch into a new answer. - cjs