I just used Apple's Time Machine for the first time on my new laptop...I wonder if everything backed up ok, what is the best way to check?
You are wise not to trust your backups until you've verified them. The history of backing up computers is littered with people who thought their backups were working fine until the day they needed them and discovered that although they never saw errors, their backups were unusable.
I recommend that you pretend like you your MacBook suffered catastrophic hard drive loss and restore your Time Machine backup to a different hard drive. Boot your MacBook off of your OS install/restore DVD that came in the accessory kit with your MacBook, then unmount your internal hard drive, plug in another external USB hard drive, and restore your Time Machine backup to that other external hard drive.
Make sure it boots and everything is intact. Not only will you be fairly thoroughly verifying your backup, you'll also be giving yourself confidence for when you do eventually lose your laptop or suffer catastrophic hard drive failure.
Don't have a second external hard drive? Get one, and use it for your offsite backup. Swap it out periodically with your primary Time Machine drive. Keep it in your safe deposit box at the bank or at your parents' house or friend's house or at work or any other site than where your laptop and your main backup drive usually reside.
If you don't get an error, then everything backed up properly. Your ability to restore the backup, though, really can only be tested by actually trying it, perhaps into a virtual machine or sparse bundle.
If you're paranoid about which files got backed up, go browse the backup volume in Finder. You'll find an exact replica of your boot volume. You can run the
You need to use the
I didn't compare the root directory