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I use an app, My Work Clock for this very reason. Whether the errors are intentional or not, it makes it easy to catch them. Just audit my paystub against it's report.
Probably the simplest is My Work Clock
> Only question I have is for documenting time; do you have any suggestions for apps or anything?
If you're on Android, yes. For tracking general working hours I use My Work Clock. It's simple, it's effective, and yet it has functionality for things like lunch breaks, multiple jobs, overtime, it's great. It can also "back up" to a Google Calendar for you. It can spit out CSV reports, and back up the database to your email.
For tracking individual projects I use Timesheet. It's a bit more sophisticated, but it's never "heavy." It has an Android Wear companion app so you can punch in and out of projects in your wrist, you can tag what you did, where you did it, track mileage, notes, all sorts of over-the-top information I really don't need but is awesome to have as an option. There's also an NFC plugin so you can get a bunch of cheap NFC tags and program them with different projects, so all you have to do is wave your phone over them to punch into or out of jobs. It offers auto-backup to Google Drive and Dropbox, and they just launched a web interface here you can also back up to (but that one will cost you). Lots of ways to export this information, what information it will export, and how you want to share it.