Before anything else, you'll want to figure out how much you're willing to spend on a new mini Bluetooth speaker. Value priced wireless speakers continue to improve, so you can find good "cheap" Bluetooth Bluetooth speakers from Chinese brands like Tribit for not too much money (less than $60). But if you're looking for a more premium speaker, you can expect to pay $100 or more, especially for more premium models that deliver better sound.
Bigger speakers tend to sound better, delivering bigger sound with more bass. But going bigger means they weigh more, which can make them a little harder to carry around. So you have to balance size with performance if you're looking for something that's easily portable. If you're interested in a larger portable speaker, one feature worth looking out for is a built-in handle.
Many Bluetooth speakers now are now fully waterproof and some fully dust-proof. If you're planning on taking the speaker with you to the beach or on a hiking trip, having a more durable speaker is a desirable trait.
Some speakers have a built-in microphone that turns them into a speakerphone when making calls on your cell phone. However, many speakers don't offer that feature. So choose accordingly if that's something you're looking for.