My book is Differential Forms in Algebraic Topology by Loring W. Tu and Raoul Bott of which An Introduction to Manifolds by Loring W. Tu is a prequel.
I am making this as suggested here An old "list question" edited to include other points based on my rejected edit of another post containing some mistakes Some possible mistakes in Bott and Tu much like this one Errata for Atiyah-Macdonald
Please post any others you've found. I'll start.
In page 18 (proof of Example 1.6), they claim "there are no constant functions on R1 with compact support" when they should have said "there are no nonzero constant..." This is confirmed in this question.