I know it's been brought up to death but there really is something counter-intuitive about Joker getting those specific tattoos. He couldn't have done them himself so he had to have sat in a chair with a tattoo artist and said "like this, a big fucking grin on my arm. Put that shit on my belly too."
"Nah, not straight, make the HAHAs kinda kooky and uneven"
"No, I don't like that font. No, not that one either. Yes, that's how JOKER should look!"
Neatly planned tattoos seem oddly sane for someone who is supposed to be so erratic and unpredictable. Self induced scars, cutting, or brands make more sense to me.