Last week I entered the wrong date and corrected it, but the data problem message persists.
Nevermind. Got it fixed. Had to delete the event, not just correct the date.
Sometimes when you change a date or place, the associated standardized date or place gets "too slow on the uptake" and fails to change. Hints and alerts use the standardized value, not the displayed value, so they'll continue to yell.
To remove the alert in a less-drastic way than removing the entire conclusion, you need to fix the associated standard: edit the conclusion and choose the correct standardized date or place from the drop-down.
Notice that the display date and standard date are off by a century in the screenshot. This is the sort of mismatch that can creep in when editing a conclusion. This particular one -- if I had saved it -- would have gone mostly unnoticed, as it's the standardized value that's correct; it's much more common the other way around, where the displayed value is completely correct, but all of the algorithms continue to yell, because the standardized value (the bottom of the two fields) is not right.
See also Áine's reply in this thread about a related or similar problem: https://community.familysearch.org/en/discussion/comment/426584#Comment_426584.
There have been several questions this week about dates doing strange things. Since these all seem to stem from not having a clear understanding of how dates get entered and stored in Family Tree, I threw together a brief presentation on how to enter and edit dates that I hope will help. I'm posting this on the other questions about dates as well.