I just played one of these missions for the first time and was quite confused:
- I had no clue that I wasn't supposed to kill the "non-anachronisms". There were a bunch of background water towers I could destroy and thought I was looking for stuff like that in addition to the out of place monsters I was supposed to track down. (More explicit directions would be very helpful for future noobs.)
- Right after I started the mission I saw the "Fix 10 anachronisms" message at the top of the screen, but it very quickly went away and I was left going around the cave killing all the monsters and destroying the water towers, but I never saw the count again, or any other messages. Finally, the cave was cleared out, but nothing happened, and I had no clue what was supposed to happen until I came on this forum and read this thread.
Apparently, I must have killed a non-anachronism monster right at the start, but it never gave me the "defeat!" message, so I just kept on clearing out the entire cave.
Anyway, after reading this thread, I realized what happened and hoped to restart the mission as x4000 mentioned, so I exited the cave, warped out of the mission, and the mission building was gone. This was definitely a world map mission, but I only got the one (failed) chance at it.