What happens if a letter of recommendation contains incorrect info about me?

To be honest, I would consider this to be a major flaw and almost certainly invalidate the letter. It may bring to attention the rest of the application, including the potential that it may be invalidated, too.

In my university, I was faced with a situation in which the reference letter had a discrepancy with pronouns. The applicant was female but the referee was writing using male pronouns (ie., he, him, his). We ran the letter through TurnItIn and found that the letter was cribbed from a source from the Internet. The entire application was rejected.

Admittedly, this is an extreme case. Still, it will raise red flags about your application. Our assessment team is rather experienced in these sorts of issues.

I recommend revising this if possible.

You are in charge of your application, including (at least some of the contents of) the recommendation letter.

You can, and should, make the professor's job easier by providing all the information about yourself in a single file. Include basic information (such as the fact that you are an undergraduate student), gently remind him of the project that you did with him by including a copy of your project, provide your statement of purpose, CV, transcript... everything that you can think of. In addition, provide a short summary (format this so that it is easy to read!)

Insist on getting an email from him when he has submitted, and when you do get such an email, immediately follow up (preferably in person) by checking that the basic information is correct, while the letter is fresh in his brain.

If all of these precautionary steps do not put your mind at ease, then perhaps getting a letter from this professor is not worth the trouble, since this will show that he does not care about your career -- if he thought that you were the next superstar, he would not be this forgetful. Getting a letter from such a person cannot possibly carry that much weight.

I agree with the rest that if the selection committee sees these factual errors, it will put the whole application under thorough check (if not discarded right away).

What I would do in your place is correct the recommendation letter that he sent you and send it back to him. That will allow him to take a quick look you haven't changed anything critical from his perspective (e.g. didn't add "he's the best student I ever had"...), sign it and send it back to you. That's in general easier for professors that have a lot in their mind or they are too busy to check this kind of "details".