It is important to acknowledge past indiscretions in an upfront and honest manner.
Typically, the application will ask if you have ever been charged with a felony or crime -- this excludes minor traffic violations; however, DUI and DWIs are taken very seriously. It may also ask if you are a litigant in an ongoing court procedures, or if you have ever been court martialed. Also, the application will ask if you have ever been placed on any sort of disciplinary probation by your undergraduate institution. Be truthful because law school's will see this in your transcripts, you will be asked to further explain if you indicate a yes to any of these questions.

Usually, minor violations of school policy (noise complaints and drinking violations) are not taken too seriously. In my case, I go to a dry campus and live in on-campus apartments. A few of my friends and I were drinking in a room and got caught by the university police. All the students were of age and no one had any legal charges pressed.
In my applications, I simply added a statement explaining my situation, and detailing how I learned from my mistakes and am currently in good standing with the university. You can upload a document like this to your LSAC profile and add it to every application you send out.
Law schools don't take such small violations too seriously; however, academic probations are of a much more serious nature. Plagiarism, getting caught cheating, or having a low GPA for several semesters can hurt your chances of getting accepted, but it is absolutely necessary to adequately explain your situation.
Always be truthful and upfront with your applications. If you aren't able to sit the bar later on because of character problems, it can save you thousands of dollars in tuition now.
(Image from Greenwhichroundup.com)