As far as your issue goes, there unfortunately isn't a quick or simple workaround that I can think of at the moment to fix this. The problem is that the WordPress hook I'm using to load the content can be used in a number of different places (including the recent posts module you're using), and since this hook can't be reliably deactivated without breaking the module on some sites with other plugins installed, I have to figure out a different way of loading the comment. I actually encountered this same issue in a plugin I'm actually developing for Diverse Solutions. Once I figure out a way to work through it, I'll port the fix over to Local Market Explorer.
Within the next few days, I plan on switching the plugin to a donation-supported development module where donations from the community will fund further development of the module. You'll see a public notice in a couple of places once the donation system has been set up.
Additionally, I'd appreciate it if you could detail your issue at the User Voice page I set up for the plugin. You can find it here: localmarketexplorer.uservoice.com. That way I'll be able to easily mark off once it's done.