I cannot comment on answers other than mine, the link "Comment" is only visible for my answers.
Is it a matter of the reputation score (as "Downvoting" is)?
If you mean on StackOverflow. Yes
On Meta you can comment on anything. On StackOverflow, SuperUser or Serverfault, you must have 50 reputation to comment.*
* Except on your own questions, your own answers, and any answers to questions you've asked. You can comment on your own "stuff" with 1 rep.
See the FAQ