I know there's a word for it...when you combine two ideas or things that really don't belong together? I think it might be a Logic term. Thanks!
Juxtapose doesn't have the sense of mixing things together, rather, you have two (usually contrasting) ideas/groups/objects/etc. side by side and are playing them off against each other.Hmm.
Juxtapose springs to mind here.
Although it lacks the mistakenly connotation.