Lucy writes, "I have recently met a man from Australia and I plan to marry him. I would also like to file the paperwork for his green card. What is causing me some anxiety is that I have a few black marks in my background. DUI, public intoxication, speeding tickets, and an arrest (charges were eventually dropped). How will this affect my petition? Can there be a denial of my petition? What can I do so that there are no problems?"
In general, the decision to allow a US citizen to marry and sponsor an alien has very little to do with his or her criminal background. The main thing that the USCIS is going to look at is the immigration history of the spouse, criminal history of the alien, your ability to support him (though his income if he is working can be added to the financial support documentation), and whether or not your marriage is genuine. It is likely that the USCIS will run a background check on you as well and your criminal record will raise red flags in the sense that the officer will suspect that a lawbreaker is more likely to break laws again. So be prepared for intense scrutiny of the validity of your marriage and very close examination of the documents that you provide. You may also be grilled more aggressively during the interview.