I just discovered that the postdoc application I submitted two days ago contains a typo. It's likely due to accidentally touching my keyboard before the final compile. I mistakenly added a character to the journal name where my manuscript is currently under review. Should I send an email to the prospective professor to correct the typo?
No, you should not send an email to correct the typo.
The professor probably receives dozens or hundreds of emails every day, and an additional email to bring up a tiny mistake will likely not be appreciated. We all make typos sometimes. There is a chance they won't even notice, but if you send the email they definitely will notice.
I always thought typos were disastrous-- until I sat on a committee reading applications and selecting candidates for a major fellowship. Absolutely no one on the committee cared at all about a typo (or typos) on an application. The content was key, not the minor errors. So don't worry about a typo, and there is no need for you send a follow-up email.
In contrast to another answer here, yes, I think you should send that email. A postdoc application is important enough to warrant a follow-up. For a casual mail, probably not.
Sending this shows that you are aware of the error and not ashamed to admit to an error. That is a better message to send than that you are oblivious.
Just add that you are sorry you didn't notice before you hit "send".
I wouldn't be bothered at all receiving such a mail. Just keep it short.
If that paper is an important contribution that will enhance your application. Send a pre-print and apologize for an apparent typo in your CV.
Otherwise do nothing and let it slide. If it comes up in an interview apologize for the oversight.
Simply sending a email with a correction of a single word carries more risks than rewards.
If you can use it to open a line of communication proactively then it will likely be better appreciated.