When you’ve just written something it’s hard to get a distance from it. Typos are easy to miss.
The best way to distance yourself from your work is to put it aside for a while. But if you have a deadline then sometimes this isn’t an option.
One way to get a fresh perspective if you don’t have time is to use a text to speech program. If you listen to your story, you’ll notice things you might not have picked up on if you just reread it.
Text to speech programs have improved in recent years and some of them sound reasonably natural. (They’ll still struggle with foreign words and names).
The ATT web site can only convert a small amount of text, so it’s not much good for reading entire stories. But it gives you an example of the capability of modern text to speech.
ATT Research Labs (It has a 300 character limit)
Natural Reader have both free and professional versions for Windows and Mac. The free version only includes one voice and it sounds pretty mechanical.
Windows software with a variety of options and voices.