There were actually two different types of rings shown in the show. In the "Pilot Movie", the top of the ring, the bezel, was curved inward [first picture, top left]. In all other episodes, the bezel is flat. A minor difference which, nonetheless, does change the overall look and feel of the ring.
This is incorrect. The top of the ring was curved inward in plenty of episodes (maybe all of them, but you aren't always shown a suitable angle and/or closeup to tell). For example, here are some screen shots showing the inward curve on the top of the early brass ring (from episodes 2.01, 2.02, and 2.03):
And some screen shots showing the inward curve on the top of the later gold ring (from episodes 4.19, 4.19, and 4.20):
The only team ring I've noticed that definitely looked like it had a flat bezel was the one worn by the Milton Collins character in Death and Taxes. I wonder if that was done intentionally to subtly distinguish it from a real team ring.