I've been using A1 Website Download to download websites which need login credentials. I was just wondering what sort of validation checks people do with the downloaded file to make sure they have downloaded the website completely and no pages are missing?

Make sure to read this help page:
http://www.microsystools.com/products/website-download/help/website-scan-login/

Geneally speaking, if you got login working and the website does not utilize complex Javascript or Ajax for is content and navigation, A1 Website Download should download the entire website (obeying the various options) if you let it run till done.

(There may be an issue if A1WD follows a "logout" link, but if you use the "quick preset" as shown in the article, many common "log out" URLs are excluded and thus not followed)

However, if you think you have encountered an issue, you can always ask here or drop an email to support