Thanks for raising this issue and for your patience while I did some testing. I upgraded one of my test sites from WordPress 3.5.2 to WordPress 3.6 using the normal Dashboard/Updates process.
I am unable to reproduce this message on my system using v1.42 of MLA.
MLA relies on the default WordPress jQuery library; WordPress 3.5.2 ships with jQuery v1.8.3, and version 3.6 ships with v1.10.2. I don’t know where an older version of jQuery would be loaded from.
I did a search for the string “blockui” and found that it is used in the wp-includes/js/jquery/ui/jQuery.ui.datepicker.min.js file.
I don’t know why disabling MLA would suppress the message, but if you give me a list of all the plugins you site uses I can do some more research. You could also try disabling other plugins to see if one of them is involved.
Finally, if the site is accessible remotely and you can give me an account that shows the problem (perhaps an “Author” account with limited privileges) I can have a look.
I regret I don’t have a better answer for you. Let me know what else I can do to help.