First, if your case is dismissed, it means you didnot commit crime as defined by law. Even if you were arrested, but the court dismissed it, you are still innoncent without criminal record. But you need to report the arrest to USCIS on your I-485 form. Coz FBI still have your arrest information on their record. If you were convicted, it means you were guilty and commited crime. If the sentence is less than 6 month jail time, you are still admissible for green card benifit. If you have more than two times misdemeanor charges (as refer to my recent posts), regardless of the final dispostion (dimissed or not, convicted or not), you need to prove your good moral character before the interview officer. I believe most officers would not care about it as long as you tell the truth. It would be very likely you would stuck under prolonged name check. Hope not.
Please refer to the following useful discussion.
http://boards.immigration.com/showthread.php?t=144728
The guy finally got his green card!