1. Bold and italics that cross contexts are handled incorrectly, because the tree structure does not support overlapping nodes (for example, ''foo'''bar''baz''', or ''foo{{bar|baz''}}). Fixing this will probably be very difficult.
2. Open tags that do not have a close tag before the parser reaches EOF are ignored, whereas some of them should be parsed (like bold and italics) and have some kind of "hidden close" flag set.
3. MediaWiki counts the occurrences of ; in the block before any text and uses this as the maximum number of parsable :s after. The current implementation only allows one : regardless of how many ;s there are.
4. MediaWiki prevents some tags from crossing certain contexts (italics and bold can't cross headings, for example) but this implementation has no such restriction.
5. The parser only recognizes a space as the separator character between the URL and its link title in [ ] tags, but MediaWiki also accepts some other syntax (e.g. [http://example.com/''Example''] is valid).

1, 4, and 5 are high priority, whereas 2 is mid and 3 is low.