I was once a wee beginning job applicant, afraid of annoying the powers that be by not following the rules. But, having now been at the other end of the table, I have a much different perspective. While there are some things that may disqualify you for a particular position, there are few acts so egregious that a hiring manager will remember your name and make sure that you never, ever get a job with anyone they know. (This is a notable exception!)
For that job where I applied 20 days too late, I told them my reason why. It wasn't even a very good reason -- I hadn't seen the job posting until that day, and it just seemed like something too good to pass up. I did not have a good excuse like Dr. Isis' correspondent. But my application was very strong and I got the interview. So it can happen. In the worst case, they don't interview you, which is the same result as if you had never applied.
Really though, unless they are a completely unreasonable person (in which case, you don't want that job anyhow!), there is no negative repercussion from applying a little late if you accidentally missed the application deadline. Now, that is not me giving you permission to willfully ignore all deadlines -- I'm just saying that honest mistakes are easily forgiven.
Job applicants often have this myopic vision of the hiring process. I was talking to one of the postdocs I'd hired and I complained about how hard it was to fill the position, how many times my offers were rejected, and how glad I was that they were there. "Oh," said the postdoc. "I only thought of it from the applicant's perspective -- it never occurred to me that you would be disappointed by people rejecting your job offers!"
Yes, we are disappointed by people rejecting our job offers! Just as much, if not more, than applicants are disappointed by not getting the job. It is a huge investment of time to screen applications, talk to applicants, bring them in for interviews, collect and evaluate feedback, and extend offers. I was so heartbroken the first time my offer was rejected. I really thought I'd had that candidate in the bag! But I had to get over it quickly and get the whole process started again.
Making a job offer is a lot like making a Jane Austen-era marriage proposal. You tell the person you really like them, they are just what you've been looking for, and you want to spend 40 hours a week together with them. You have these means to provide for them (a.k.a. a salary), and you hope to produce little hybrids of yourself and them (a.k.a. research papers), if only they find you as attractive as you find them. Then you smile nervously and hope they will say yes.
They usually have to take some time to think about your offer, and you desperately hope that they will think you are Mr. Bingley and not Mr. Collins. I've been Mr. Collins more often than I would like. In fact, I once had one person reject my job offer so that they would be free to possibly interview elsewhere (the place of their dreams, but that had not yet contacted them with any interest). I don't know if that puts me in the same league as Mr. Darcy with his first proposal to Elizabeth Bennet, but that was a pretty odd rejection to say the least. But it was all good, I offered the job to the next person on the list, who verbally accepted it immediately, and I felt relief that the position was finally filled.
After experiencing both sides of the table, I understand the hiring process much more, and at this point I am unafraid of applying for jobs (if I were in a position that I needed to do so). I know how the system works. I would know how to make myself attractive to hiring managers because I have been in their shoes. I will write another post on that topic.