I tried some of the suggested native 3rd party apps, and my conclusion is:
The mobile web application is very good and I don't see the point asking for a native application in fact. I just tried to edit some tasks offline, then switched netwok on again and the synchronization was just right.
I don't think having an additional widget, with more reminder would be great: having the synchronisation with google calendar in place is just fine, this keeps the sources of information to the minimum.
The only issue I see, is that the Google calendar seems to be a bit slow to refresh and take in account new tasks. As far as I know, the issue is on Google side.
Congratulation to the Toodledo team for keeping things simple and working on functionalities instead of trying to implemente clients for all possible platforms!
Postscriptum: as far as I know, this is the very purpose of HTML5 applications to avoid re-implmenting applciation for each platforms.