Yes we can, but we "don't modify a post such that it changes the meaning of the post."
Usually a mark is left after editing the post. This can be red or in a small font (Edit: reason..), but it's not mandatory. Moderators are not restricted in this regard.
About the post you showed as an example only Xal0lex, who made the edit, can answer though. I don't know what changes he made in the post.
If a moderator edits a post, a note like this can be used.
I believe the Moderator may likely send this as a pm to the user.
I this was different because It was shown that it was last edited by the Hal

Where as, in the image shown by Op, it's seen that the post was last edited by Xal0lex.