I applied for a job yesterday with a cover letter and CV. I did proof-read it at the time, and really tried hard to make sure that I'd proof-read it fully.
Problem is.... I looked back at the cover letter just now, and it's got some clangers in that I clearly missed when I read it over before submitting
e.g. pretty big oversights like mentioning another role for a different sort of organisation in the last paragraph 

Ironically enough, one of the skills requested in the job specification is 'very good attention to detail'(!!!) I really tried hard to make sure I'd spotted any errors, but clearly I missed some(!!!)
What do I do? Do I just chalk this one up to experience and just make damn sure I don't have any similar errors in my other job applications?
Also, this is a bit of a daft question, but do you have any advice on how I can avoid doing this in the future? I honestly don't notice any big mistakes when proofreading for the first time. It's mostly when/if I read back over my application the next day that I'll start to notice mistakes.
Is the solution to this something like filling an application, proofreading it initially and then going back to it the next day to proofread it again?
Feel so frustrated at myself :( the person looking at the application is going to think I'm such an idiot!!!