Alex here from the Shopify support team.
Many Shopify merchants use third party themes and are very happy with them! I've seen some awesome ones, personally. What you'll want to keep in mind is that the theme is what dictates almost everything that occurs on your storefront. The theme is what takes the information from your admin (products, images, collections, navigation, etc) and arranges them beautifully on your online store.
If you run into issues with your online store in the future, it's very likely that you'll have to ultimately reach out to your theme developer to fix it, as third-party themes aren't directly supported by Shopify. You can always reach out to Shopify Support first, however! We're always happy to take a look and let you know what we think, even if we can't fix the error ourselves. Some examples of coding issues I've seen in the past that have had to be sent to developers are:
Another thing to keep in mind is that any third-party apps that you add to your store to change the way it looks on the front-end will likely also edit the code. The more third-party code that is added to the online store, the more likely that there may be a code conflict or an error that arises.
For this reason, I would strongly recommend duplicating an untouched, unpublished version of your theme to use for troubleshooting - you can do this by clicking More Actions > Duplicate Theme once you've added it to your Online Store > Themes section.
Let me know if this helps, and feel free to follow up here with any other questions!
Alex | Shopify Support