I am contacting you to let you know there are a few bugs in WP-Invoice with the Stripe payment integration.
I have tested on a fresh installation of WordPress 3.8.1 with no other plugins enabled, as well.
1 - "Unknown error" while processing payment. I did not leave a trailing space when entering the keys in the setting and yes, I entered the webhook.
2 - To test the above, I decided to reset my API keys and use new keys in WP-Invoice, then I got the error that my keys were expired. I went hunting in the database and it seems that not all instances of the Stripe keys were updated when saved. References to my old keys are still in the database.