Before posting this, I first searched meta, and found that previously people already found the accept answer checkmark unclear.
The accepted answer indicates that a change was made, but I still find the checkmark the worst from all the SE sites I am on. I actively notice me wondering whether or not I accepted a certain answer. I find an outline to be far more clearer.
Usually I'm only certain after comparing the color with another answer (if there is one!). An outline vs. filled in shape would solve this.
Additionally (this isn't done on any SE site I'm aware of) I feel it would also be an improvement to switch the image to the 'checked' state when hovering over it when it isn't checked.
Futhermore, a GUI should be consistent so a user can expect a certain behavior. Therefore I would argue to definitly change the accept answer icons to something similar as the upvote/downvote/favorite icons. They look wonderful, and also use the outline when not selected. I asked about this on UX.SE.
Following the same argument, I would either implement the hover for all icons, or for none ...