Thank you both for your responses, however we are still having an issue with this.
Rincy, first-off we are primarily using Chrome to develop in Pega 7.x. I did confirm the ActiveX control security level as mentioned in the 2nd article you linked, and that wasn't the issue. As for the first article, I don't believe VML is used in Chrome or later versions of IE, both of which were rending our flows just fine in Pega 7.1.9.
And DharanitharanR, I tried the Revalidate and Save wizard on a few of our flows, but no change.
Any other ideas? If we are still having this problem later today, I will likely open a support ticket.
Resolved! This issue was resolved when we discovered that the upgrade script for 7.2.1 had been interrupted before completing. We re-ran this script, verified that it had completed, started the application server and confirmed that the issue was resolved.