I have done the change: JQuery 1.9.1 and JQuery UI 1.10.0.
Seems Ok and stable in IE10/Chrome/FF, Admin menu is working for widgets, rules.
The useful ShapeTracing module is also working ok.

Main changes where on the obsolete method $("xxx").live(p1,p2) to replace by $(document).on(p1,'xxxx',p2)
then on the fact that jqueryUI now uses domains so data('autocomplete') became data('ui-autocomplete') or variant with item.
I attach here my new Orchard.JQuery module with the various .js changed (including some js from nawzet.ecommerce).

If somebody wants to try the changes and provide a feedback.
The code is attached to the issue here

Please do vote on the issue.

Could you try to edit some date/times like the field or Publish Later part ? Last time we tried to upgrade they were causing issues.

Editing the dates in CommonPart seems Ok: the javascript widget is working perfectly (and quite nice) and the value stored in DB is OK.
And DateTime fields are Ok.

I am now using this since 15 days with the last source code and everything is OK. Hope it will be included in 1.7.

Is anyone using the Mirgrate Plugin? Just a suggestion for extra measurement... I found it really useful for testing.

I included it in the module evolution I proposed, useful but in fact very changes to do.