Not really. The “Skip Intro” feature is largely out of our control. I wish that not only would it be more easy and obvious on how to force a skip intro check, but that we had some control over fixing incorrect intro markers themselves.
The only advice I have are as follows:
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Plex seems to try to analyze for intro when I analyze episodes in bulk. This does not mean I click the triple dot on an entire season or show and hit analyze, I mean you must go into a season, and select each episode by clicking on the circle that appears to the left of the poster when you hover the mouse over it. Once you select each episode, try doing an analyze by clicking on the new menu that appears up top in yellow and choosing analyze. You can quickly select all items in a season by pointing to the text that lists the number of episodes, and clicking the circle that appears there.

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If all else fails, try to plex dance the show itself. Nuking the entire library is a bit much, but a quicker method is to dance the show (or just the season) itself. I’ve had some success getting the intro markers corrected when I danced the files. Method #1 up above might work as well now, but the old way that I know works (if it works) is the dance.