PayPal has now acknowledged this as a current issue on their status site:
Impact to Payments Standard (PP-LIVE-8276)
Incident Start: Apr 12, 05:51 UTC
Incident End: On-going
We are experiencing an issue which is affecting Payments Standard on the Production environment. Some users may be encountering the error message "Things don't appear to be working at the moment. Please try again later" when attempting a checkout.
Our technical teams have been engaged and are actively troubleshooting the issue.
Apr 12, 20:16 UTC