Real people, real devices, on-demand.
We've already made this point in a crowdtesting tip (Know Your Users), but it bears repeating in the exploratory testing context.
Because exploratory testing relies on the experience and engagement of the tester to develop, execute, analyze, and report software tests, consider using testers who more closely match your customer profile. Doing will give your testing cycles a better chance to surfacing the kinds of bugs and interaction problems that your users will tend to run into.
Whether it's language skills, profession, tech-savviness, geography, age, or gender, these characteristics influence how people use software and how they think about your app or website. Take the time to figure out what kinds of customers you have and apply this to your software development and testing. Combine this with experienced exploratory software testers, and you're on your way to thoroughly-tested software.
By putting in the effort to do exploratory testing with real people who resemble the ones you're building your product for, you'll get better quality bugs, get more targeted and qualified feedback, and you might even catch some audience-specific usability issues that might otherwise have flown under the radar.