The following is a first draft trying to describe the Wikitext-Syntax with Extended Backus–Naur Form (EBNF).

Features of current parsing that must be incorporated (list is likely incomplete):

1. Redirects
2. Headers
3. Paragraphs
4. SGML (HTML, nowiki, math, plugins)
5. Lists (unordered, ordered, definition, pseudo-definition)
6. Initial spaces
7. Bold/italics
8. Templates (int:, msg:, msgnw:, raw:?)
9. Template parameters (both on the sending and receiving sides)
10. Horizontal rules
11. Magic words
12. Wikilinks (category, image, Media:)
13. External links
14. Plain URLs (e.g., http://blah)
15. Tables
16. Character entities (e.g., &, Ӓ, ሴ)
17. Behavior switches
18. Date reorganization based on user prefs
19. ISBNs

General

digit         = ("1"|"2"|"3"|"4"|"5"|"6"|"7"|"8"|"9"|"0");
URL           = { ASCII letter }, "://", { URL char };
ASCII letter  = ("a" | "b" | "c" | "d" | "e" | "f" | "g" | "h" | "i" | "j" | "k" | "l" | "m"
                | "n" | "o" | "p" | "q" | "r" | "s" | "t" | "u" | "v" | "w" | "x" | "y" | "z"
                | "A" | "B" | "C" | "D" | "E" | "F" | "G" | "H" | "I" | "J" | "K" | "L" | "M"
                | "N" | "O" | "P" | "Q" | "R" | "S" | "T" | "U" | "V" | "W" | "X" | "Y" | "Z");
URL char      = (ASCII letter | digit | "-" | "_" | "." | "~" | "!" | "*" | "'" | "(" | ")" | ";"
                | ":" | "@" | "&" | "=" | "+" | "$" | "," | "/" | "?" | "%" | "#" | "[" | "]");
Unicode char  = (* Assume this is all valid Unicode characters. *);
text          = { Unicode char };

full pagename = [ namespace, ":" | ":" ] pagename;
namespace     = Unicode char, { Unicode char };
pagename      = Unicode char, { Unicode char };

Links

start link    = "[[";
end link      = "]]";
internal link = start link, full pagename, ["|", label], end link, label extension;
external link = URL | (start link, URL, [whitespace Label], endLink, label extension);
redirect      = "#REDIRECT", internal link;
header link   = "/*", text, "*/";
ISBN link     = digit, ["-"|" "], 3 * digit, ["-"|" "], 5 * digit,
                [("-"|" "),(digit|"X"|"x")];

Headers

header end  = [whitespace], line break;
header6     = line break, "======", [whitespace], text, [whitespace], "======", header end;
header5     = line break, "=====",  [whitespace], text, [whitespace], "=====",  header end;
header4     = line break, "====",   [whitespace], text, [whitespace], "====",   header end;
header3     = line break, "===",    [whitespace], text, [whitespace], "===",    header end;
header2     = line break, "==",     [whitespace], text, [whitespace], "==",     header end;
header1     = line break, "=",      [whitespace], text, [whitespace], "=",      header end;
comment     = "<!--", [text], "-->";
commentary  = "<comment", [text], ">", [text], "</comment>"; (* This works? *)

Formatting

horizontal rule  = "----", {"-"};
bold italic text = "'''''", text, "'''''";
bold text        = "'''", text, "'''"; 
italic text      = "''", text, "''";
code line        = linebreak, " ", text;
nowiki           = "<nowiki>", text, "</nowiki>";

Lists

unordered list           = "*", text;
continue unordered list  = (unordered list|continue unordered list|":"|"*"|"#"),
                           linebreak, unordered list;
ordered list             = "#", text;
continue ordered list    = (ordered list|continue ordered list|":"|"*"|"#"),
                           linebreak, ordered list;
definition list          = [text], ":", text;
continue definition list = (definition list|continue definition list|":"|"*"|"#"),
                           linebreak, definition list;

Signature

user signature           = "~~~";
user signature with date = "~~~~";
current date             = "~~~~~";

Includes

include  = ( template | tplarg ) ;
template = "{{", title, { "|", part }, "}}" ;
tplarg   = "{{{", title, { "|", part }, "}}}" ;
part     = [ name, "=" ], value ;    
title    = balanced text ;
name     = balanced text ;
value    = balanced text ;
balanced text = text without consecutive equal braces, { include, text without consecutive equal braces } ;

Behavior switches

place TOC            = {whitespace|linebreak}, "__TOC__",           {whitespace|linebreak};
force TOC            = {whitespace|linebreak}, "__FORCETOC__",      {whitespace|linebreak};
disable TOC          = {whitespace|linebreak}, "__NOTOC__",         {whitespace|linebreak};
disable section edit = {whitespace|linebreak}, "__NOEDITSECTION__", {whitespace|linebreak};

Tables

table start       = "{|", {style|whitespace}, linebreak;
table end         = "|}";
table caption     = "|+", text, linebreak;
table header cell = (linebreak, "!", ({style|whitespace}- "|"), text)
                  | (tablecell, ("!!" | "||"), ({style|whitespace}- "|"), text);
table cell        = (linebreak, "|", ({style|whitespace}- "|"), text)
                  | (table cell, "||", ({style|whiteSpace}- "|"), text);
table row         = linebreak, "|-", {"-"}, {style|whitespace}, linebreak;

table body        = ( table header cell | table cell ),
                    { table row, ( table header cell | table cell ) };
table             = table start, [table caption], [table row], table body, table end;