First of all, forget about my comment regarding «« and »», I was under the impression that they were common on most keyboard layouts but they apperently aren't, so I take that back, it's not a good idea.
I've gone over your proposal more thoroughly so here are some more detailed, comments:
* Regarding your style of headings: It's currently possible to make the html equivalent of <h[1-6]> with wikisyntax, but you specifically disallow level one (=) headings which is insufficient, remember that not everything is an article where you get the first heading generated for you, special pages and other extensions might want to make their own first heading (other than the one made with use of the title object) using wikisyntax and there will be no way for them to do that save for falling back to spitting out HTML, furthermore level one headings are in wide use on pages like the English Wikipedia's Village pump, why do you want to deprecate it? Presumably it clashes with something else I haven't noticed.
* I like that one newline no longer terminates a list, however this syntax will not be complete without allowing <p> since there will be no way to make paragraphs within a list item.
* I don't like your definition lists because they're exactly the same as the current ones and encourage using ":" for indenting, if you're going to indent something like
: Indent
<dl><dd>indent</dd></dl> is not the best way to render it, it may be legal XHTML to omit <dt> and take advantage of the fact that <dd> is indented by what would be approximately a tab in most (if not all) browsers, but it's certainly far from the way it should be done™.
* Using [[]] for external links means that in practice we won't be able to have articles/pages with titles like "http://foo" although [htp:/fo] are all legal characters in page names (not really that big a disatvangage, and I like it better than [])
* Just so we're clear you want [[stuff|like|this]] to generate (approximately) <a href="stuff" title="this">like</a>? I don't really see the point, but I suppose it doesn't hurt since it extends the previous syntax gracefully.
* I like the [[Foo (bar)|]] syntax, we currently do support that but transform it (as Rowan Collins pointed out) at savetime, however I don't see any good reason why it shouldn't be a valid part of the syntax.
* I don't like the named arguments for links, It would clash with the current namespace of links (i.e. does [[target=foo|text=bar]] point to "foo" or "target=foo" ? How about [[asdf=foo]] ? ) I think it's overdoing it, let's have one syntax for each action.
I like where you're going with the image syntax but I don't like it *quite* enough to really like it, I'll explain: What I don't like about our current image syntax is that due to the way it's all cluttered up it's hard to extend, yours is better but IMO not quite good enough, for example I'd like to have (comments begin with #):
<<begin image>> file=pl_bulet.png style=frame # instead of just "frame", no "magic words", just attributes=values width=5em caption=Logo <<end>>
Note however that since = has a special meaning caption would always have to come last if you wanted to write something like:
caption=You can make captions in MediaWiki with caption=foo
Or alternatively the parser would have to be smart about it.
* I like the whole <<>> thing, but I'm not sure about the added complexities of using it for comments too, how about <<comment like this>> (just an extension named comment that ignores its input) rather than << like this>> (i.e. to make << *.*?>> comments), or just the old <!-- -->
* I was sceptical at first about the new {{}}, but I've come to like it, any "decent" article on Wiki(pedia|media) seems to have infoboxes and other things that require some kind of inline CSS styles and eliminating all that in favor of a pure wikisyntax solution would be nice indeed.
* I like // ** ^^ $$ and __, note however that since * is used for both lists and bold the parser would have to break a case like "***foo**" down by looking for the closing ** at the end of the line to see if it's dealing with a first level <ul> or a third level <ul> (not that big a deal, we do that already in a way with ''' and '')
* Aside from the advantages of the new {{}} they're just like our current tables, except for one thing, the new ^ and < syntax, I love it, I think it's a very simple and intuative solution to the problem of colspan/rowspan not being obvious enough.
P.s. Of course the french will hate it, but that kind of given..