Sending official transcript with mistakes
Would it harm my application if I sent this transcript?


Not if done correctly. This is one of those "special circumstances" where there is likely no established rule; you just have to contact a human and explain the situation. What you can do is:


Send the transcript with the errors
Reach out to the person in charge of admissions (either the professor and/or an administrator) at the University and explain that there is an error on the transcript.
Reach out to someone at your own University to see if they can send some kind of official notice to verify that there is an error.


Once everyone is aware of the problem, it should not be an issue. They can verify with your university that the transcript is indeed an error.

Of course, the best solution would be to contact your university to see if they can remove the errors and correct the transcript. But if this is impossible, then the above should be good enough.