I'm having exactly the same problem. The mailchimp widget doesn't seem to "close" itself properly - result is that the bottom dive I use to display a border image doesn't show and all the HTML below the widget is thrown out.
I strongly suspect it has something to do with a trailing character at the end of their widget code. All my other well behaved widgets end with:
The mailchmip widget ends with:
Note the extra } character.
If I remove it the widget breaks but it is useless to me on any number of themes as it is as it screws up the subsequent sidebar code.
If anybody who knows about these things could suggest a work around I would be very grateful. Mailchimp are usually excellent to work with and I was expecting this plugin to work flawlessly so I'm very disappointed to see that they are not actively addressing it here.
Sure it's fine to say it tests OK on a vanilla theme but I've never had this sort of problem - replicable across many custom/premium themes - with any other widgets I use so surely they could sort this out for the WP community - and their customers!