The short answer is: there's nothing you can do, if the user is sufficiently persistent. There are some simple things you can try, but to be realistic, there's no guarantee any of them will work; you might just have to live with the situation.
You can and should continue to monitor all questions and answers as they come in. When you see a bad question or answer, you should downvote it, regardless of author. Keep downvoting bad questions and answers as you see them -- but remember that StackExchange doesn't want you to try to search out this user's other questions or answers.
You can try leaving comments on this user's bad answers. But be realistic: users that fit the profile you describe often aren't going to change their behavior because of comments; and it's too easy for other readers to fail to see your comments or to sympathy-upvote the answer nonetheess. Leaving comments is a worth a try -- it might work -- but don't be too disappointed if it doesn't change much. Also, understand that reactions to critical comments can vary. Some people get very offended or upset, or think you are being rude (you're not, but what can you do?) and start attacking you. If you see that happen, you'll have to decide whether it's worth it to continue commenting. Personally, I've learned that leaving a critical comment often isn't worth the agita, unless I recognize the user and consider them thoughtful; so in many cases I'll just downvote without commenting.
Ultimately, once you've tried the basic things, if they don't work, there's not a lot you can do. You'll just have to accept that this is the way things are. The StackExchange site is pretty good, but it's not perfect, and sometimes it promulgates bad answers and bad information. Right now, there's no solid solution to the problem you outlined; there's no mechanism that's really effective, if the problem user is enthusiastic and prolific enough. Oh well. Hopefully people won't rely upon StackExchange alone for anything that's life-critical.
It's possible to become demoralized and frustrated by the situation, but I think the most healthy response is to realize that not all problems can be solved; to realize that the StackExchange platform is not perfect, but it's still better than any of its competition. Keep your eyes on the positive aspects of the situation: even if the site is not perfect, by participating in StackExchange sites, you are doing a net good for the world.
In the long run, perhaps the best bet is to try to grow the community of your site so its population is, on average, more knowledgeable and more expert. That will help improve the quality of answers. One of the best ways you can help with that is by improving the quality of the site overall and by making the site attractive to experts.