I would go to Advanced Metrics, set my time frame, choose the Forum Topics metric, then do another for Accepted Solutions. The number of threads that had replies that have not been marked as an Accepted Solution will be the first result minus the second result. A relatively simple calculation.
Hope that's helpful.
So, any idea how to export the text of those replies where there wasn't an accepted solution? We want to review the replies.
It sounds like you only have community (not Response). But, if you had a Response (aka LSW) instance and your Community was connected to it via the Lithium API, it's really easy to get the data you're looking for. I'm posting in case you or anyone else is in that situation.
You'll need to create 1 tag first:
Create a tag that has a lucene rule to look for "Re: " (literally, with the quotes). We'll call this the 'reply tag'.
Then you'll need to create a new smartview with these attributes:
"All of These" - enter "Source > Lithium" tag, so you're just looking at conversations pulled in from your lithium instance.
"Any of These" - enter your 'reply tag'. So you're now looking at community threads that contain "re: " in them. They're threads with replies.
"Exclude These" - enter "Annotation > Accepted solution". This is a system tag. Now you've excluded all conversations with an accepted solution.
In analytics you can view the smartview and can view all conversations that meet its criteria, and open each individually.
I learned this and a whole lot more by working with Meg Hahn @ Lithium. She is fantastic.