I recently started a new job, and the man who is supposed to be training me is instead using me to pass off his own shoddy work. He'll email me something that I know is not up to speed - but he has not yet taught me how to fix it - and then have me email it to the rest of the company from my account. This feels a bit like sabotage. Where's the line?
There are very few personal office problems that cannot be solved - or, at the least, greatly improved - with a mano-a-mano conversation. Unfortunately, this is one of them.
Your trainer is using you, and your unofficial "honeymoon" period as a new employee, to cover his own laziness. He knows that sloppy work coming from you is understandable - and almost forgivable - because you are a novice at your position.
It's time to go over your trainer's head and make the scary walk to your supervisor's office. As the new guy, you don't want to come off as a tattle-tale, but this man is ruining your reputation before you can build it. Plus, he's supposed to be mentoring you, and instead he's conning you. You need to put a halt to this situation and get yourself a new trainer as soon as possible.
Don't feel bad about offending this guy. He knows what he's doing, and he's probably already got a plan for how to cover himself if he gets caught. The world is full of too many short-cut artists, those guys who think their most important job is finding the way to do the least amount of work and still fulfill their job duties. The less you associate with this sort of behavior, the better.
Bring examples when you go to your supervisor. Don't lay blame, but make it clear that you don't want to put your name on any work that is not up to your standards. Your ethical stance will say a lot about you, and should play well in front of your new boss.