The Mahdi does not have an easy time battling the Dajjal. According to the hadith, the Dajjal runs the entire world (except for Mecca and Medina) and has almost unlimited wealth and resources, while the Mahdi has a small but devout cadre of followers; he has many setbacks, but eventually destroys the Dajjal (with help from 'Isha).
Here's a nice hadith telling people how identify the End Times by the moral climate. No, this is not from a sermon by a Southern Baptist televangelist. It is an "authentic" hadith (a hadith that Muslim scholars accept as non-spurious).
When you see that truth has died and people of truth have disappeared,
and you see that injustice prevails through the land;
and the scripture has become despised and things are introduced into it that are not in it and it is turned towards men's desires;
and you see the people of error having mastery over the people of truth;
and you see evil out in the open and the doers of evil are not prevented nor do they excuse themselves;
and you see moral depravity openly manifest and men being content with men and women satisfied by woman;
and you see the believer silent, his word not being accepted;
and you see the sinful lying and he is not refuted nor does his deceit redound upon him;
and you see the lowly despising the great;
and you see the wombs cut open;
and you see he who boasts of moral depravity is laughed at and is not spurned;
and you see young men being handed over like women and women cohabiting with women and their numbers increasing;
and you see men spending their wealth on things other than pious deeds and no one opposes or hinders them;
and you see the onlooker turn his back on the efforts of the believer;
and you see one person molesting his neighbor and no one prevents it;
and you see the unbeliever joyful because he does not see gladness in the believer when he sees corruption in the world;
and you see alcoholic drinks being drunk openly...
and you see women occupying places in the assemblies just as men do and usury is carried out openly and adultery is praised...
and you see the forbidden things made legal and the legal things forbidden;
and you see that religion becomes a matter of opinion and the Book and its laws fall into disuse;
and you see the leaders drawing close to the unbelievers and away from good people;
and you see the leaders corrupt in their rule;...
and you see men eating what their wives have obtained as a result of their immorality and knowing this and persisting in it;...
and you see places of entertainment appearing which no one who passes them forbids them and no one is bold enough to put an end to them;
and you see a worshiper only praying in order that the people may see him;
and you see the experts in religious law devoting themselves to things other than religion, seeking the world and leadership;
and you see the people living together like animals;
and you see the pulpit from which fear of Allah is enjoined but the speaker does not act in the manner he has enjoined others to act;...
and when you see the tokens of truth that I have taught, then be aware [of the advent of the Mahdi] and seek salvation from Allah."
-- The Sixth Imam Jafar As-Sadiq (as)
It reads almost like the table of contents for the latest book published by Regnery Press.
BTW, when I say that thie above hadith "prophecy" (or any other -- say, that fire would fall from the sky upon Bagdhad), I do not mean to lend credence to the sayings of Mohammed. These sorts of "prophecies" are simply standard boilerplate for the genre of "apocalyptic literature." But the imams are having a field day applying them to the front page of the daily news.