Yup, I think the most logical place (on desktop at least) would be before the author/last reply text.
After putting on my designer hat and thinking on it some more, I think the big issue is that with the exception of avatars, the main thread listing is almost entirely text based while the background color/inverted text of the design makes it look like a button that stands out completely from the rest of the design. Quick hack to show what I mean:
This is absolute perfection.
I understand why tags may be a good idea, but the current way to display them is far from ideal. I find tags to be more of a power user feature, that won't be necessarily used for the majority of the userbase every day, so while I'm not against them I think they should be as subtle as possible, and definitely not be in front of every thread that has one of them.