I have noticed that the moderators are marking answers now on this site. I can understand to some degree. However I also noticed there is no indication that a moderator marked the answer and not the original person that asked the question. Is this something that can be added, maybe if you have over 1k karma points or something?
Possibly, but not easily - it would require server-side work that's currently not possible given how the site's set up. I'm honestly not sure if it's something we'd necessarily want to do, as it generally proves incredibly hard to get people to mark answers on their own questions, especially where there are people signing in just once to ask homework questions, etc. I don't know that having a distinction on who accepted it would be valuable to people landing on that question in future.
My recommendation would be for moderators to stop marking questions as answered. I just ran into one where the OP was given an answer totally outside of what he needed to do and his final comment was "I have no idea of even where to begin". On top of that, my personal feeling was that the given answer was totally out in left field. Dave Green seemed to quietly agree with that notion in a previous post on that same thread. Worse yet, the habitual moderation of posting a comment telling people how this site works and suggesting that the OP mark an accepted answer is as bad as SPAM because it drives otherwise "dead" posts to the top of the heap, obfuscates the name of the last person that actually participated, and provides no real value especially since it doesn't seem to be working to get people to mark accepted answers.