It is very difficult to distinguish the discription of the acheivments of the Messiah from that of the messianic age during which the Messiah will rule. In some cases, it is possible that these things will be accomplished as a way of preparation for the arrival of the messiah. Nevertheless, here is the best list I can supply:
- He will bring all the Jews from the far ends of the earth back to the land of Israel. Or simply, the Jews being in the land of Eretz Yisrael will be a condition of the Messianic age. This has begun, but has not been completed, thus the Messiah is not yet come.
- He will be descended from the line of Judah.
- He will "be" King David, meaning not only will he be a direct descendant of David, but more importantly he will rule Israel from Jerusalem like David did--none of the candidates for Messiah have fulfilled this so far.
- He will be a great warrior.
- He will bring world wide peace between the nations--this has yet to happen.
- He will be a just judge
- The temple will be rebuilt, either by the Messiah, or in anticipation of his arrival. The temple will be a house of prayer for ALL people.
- During the Messianic age, all people will know God and will automatically keep the commandments appropriate to them.
This is an all or nothing deal -- if a candidate does not fulfill even a single one of these criteria, they are not the messiah. And saying, "Oh, I'll just do it the next time I'm here, or I'll take 200,000 years to do it" doesn't cut the mustard either. They are to do it in their lifetime. I mean, this is pretty simple.
That's my best job. Other writers say it in different words, or use a different organizational system. I suggest everyone google "Judaism criteria of the messiah" and read what the different websites say. Each point has scriptures to back them up, but it is harder to find websites that go into that sort of detail, although they are online if you search hard enough.