The phrase "serious weakness" means a significant problem or limitation that can have negative consequences or hinder someone or something. Full definition
I happen to have a pretty serious weakness for chicken noodle soup and this is seriously the best chicken noodle soup I have ever had! (thefrugalgirls.com)
In his previous shows, large paintings didn't quite make it because the scale showed up serious weaknesses in drawing. (artforum.com)
How can all those eyes fail to stay on the ball for long enough to allow the paper to be submitted with serious weaknesses? (retractionwatch.com)