Im pretty sure the third level of dead eye lets you mark the x's yourself not positive about this though. Also yeah it was kind of annoying trying to complete missions and then running over a dog with your horse and getting a bounty on your head. Still a pretty decent game though.
I kept getting bounties whenever I "solved" the random scenario where some woman is getting attacked/kidnapped. According to my own code of ethics, I'd just shoot the perpetrator in the head (or in a piece of real estate a bit south of there), but apparently my response was excessive, because spectators decided to brandish weapons/open fire. The first time it happened, I'd figured they were a gang or something, so I put them all down fast, and found myself wanted. That ticked me off, so I killed my way through town and loaded my last save.
Now, I just lasso the attacker, hogtie him to complete the mission and get my honor points. Once the lady runs off, I pick up the hogtied assailant and either ride him out into the woods to slit his throat, ride out in front of the train and set him on the tracks, or I'll let him go and lasso his neck again before dragging him behind the horse (sometimes slinging him of a cliff/dropoff when one is available), which is also how I deal with horse thieves.