To see the problem just copy the unordered lists example given in the Markdown plugin documentation into a new buffer and attempt to render it. An embedded unordered list is created correctly for the sub-item labelled "A subitem, indented with 4 spaces" but the item immediately preceding it has only the first word rendered. The rest of the item text is lost.
Updating the underlying libraries (pegdown, parboiled, ASM) used by the plugin appears to fix the problem. This was non-trivial as the parboiled JAR provided by the original plugin author had to be replaced with 3 separate JAR files ( parboiled-core, parboiled-java and asm-all version 4.0).