I've been using hovercards for just a few days and it's a great little feature that enhances the browsing experience. The visual design is modern and clean. Like the name as well. As always with new gadgets there are things to improve and here are some suggestions.
1. Keep it as simple for the readers as possible. Pretty much as it is right now. An editor version with extra functionality and info might be worth considering (depending on feedback) but that should not be the default version.
2. The only functionality I would consider adding is the cascading popup functionality of navpops which means that hovercards need to show hyperlinks in the text (nice to have not must have).
3. If you hover over a link at the bottom of the page the hovercards should open upwards instead of downwards
4. I often rightclick on links to open an article in a new tab (or window). During this action the hovercard appears with is somewhat distracting and annoying. Can the hovercard recognize the rightmouse click and stay closed?
5. Disable hovercards in the watchlist.
6. Disable hovercards on the view history page.
7. Disable hovercards on WikiProject pages