There are flag buttons on each image and on each comment. On images, it’s to the right of the share button above where it says who made the image. On comments, it’s next to the reply button.
There are punishment systems in place if you do get flagged too much. These involve losing your comment reputation and being unable to meme comment until it improves as well as time limits on how much you can comment period. The problem with that is malicious users will use alts to downvote/flag your good comments and trash your comment reputation. I’ve dealt with trashed comment reputations from troll attacks as well as arguments with thin skinned users with alts and believe me, it’s infuriating. Personally, I prefer to downvote sparingly and only flag if it violates TOS. If you’re really violating TOS, then we will delete your account. That’s just my two cents on it though.
Not sure what you mean by meme contests. If you’re referring to submitting a meme and trying to get it on the front page, I think the current Hot page works fine. It shows the hottest memes over the past few days and drops them out when they start losing traction.