"assuming that by the time they noticed that the content was incorrect I could have written and backdated the first document"
No! You'd honestly consider undertaking fraud (for which you'd be personally liable in most jurisdictions) to benefit the reputation of your employer (for which you get little if any credit) and for the sole reason of hiding their organisational incompetence of neither having the spec, nor the process to realise and correct this omission in the first place?
If I might offer some advice, having worked in a number of situations of institutional fraud, never, ever cover things up for the business. Unless you're a shareholding director, fraudulent practice won't benefit you, but the risk you're taken is your entire future career, and possibly your liberty. Might sound extreme for "mere paperwork", but if you were falsifying ISO9000 compliance, that compliance is presumably relied upon by customers, and the fraud will be deemed to have been done for financial advantage. And potentially the business would have been embarrassed by a blot on the audit scorecard, but that's retrievable. If they were found to be cheating the audits, then the customers simply won't renew - will your employers thank you for that?
Very few corporate frauds start off as vast and wilful attempts to steal - the vast majority are some attempt to put right a missed ambition - sales targets not met one quarter, earnings below expectations, operational KPIs below the bonus threshold. And the perpetrators usually plan to make things good next quarter or next month, conceal the evidence, and nobody will be the wiser or worse off.
And whilst your intention was to cover your tracks well enough to avoid detection, that's what people like all the jailed, sacked and unemployed fraudsters thought. Remember Enron, and Arther Andersen? The demise of the $100bn a year Enron empire, and the 85,000 employee Andersen's business came simply because the board wanted to hide a few underperforming projects, planning to make things right in subsequent quarters. The Satyam fraud reported elsewhere on the Reg today is another example.
If you're prepared to do fraudulent things, at least make sure that you personally benefit from the risks you take - but even then I'd say don't do it. I've worked in an IT firm with people currently doing time for a fraud they hoped they could hide, but that benefited them.