As a layperson and not a historian, it seems to me that the methods of persecution just seem completely ineffective and laughable.
This is Rome we're talking about, an empire that could field several armies at once at four different corners of the continent. And even the most anti-Christian emperors such as Decius II and Diocletian couldn't come up with a coherent way to stamp out a tiny sect that almost everyone disliked? How hard could it have really been to deal with such a small and powerless minority?
Note: I understand and can excuse the poor effectiveness of persecutions by some emperors. Nero, for example, just wanted a scapegoat to momentarily distract the angry crowds. But I feel that some of the more dedicated anti-Christian emperors (such as the two I mentioned above) should have been intelligent enough to design more effective methods.
Maybe I'm simplifying this too much. In which case, please enlighten me. Thank you.
I started to write you an answer a while ago, but then I thought better of it, but I see there is some interest in your question.
Firstly, you need to understand that the Roman Empire didn't function like a modern nation-state, and a lot of the political and governmental apparatus didn't exist. Yes, Rome fielded large armies, but it didn't field large bureaucracy, and so a lot of what government officials did was executed through their own personal means.
Secondly, persecution was indeed haphazard, because it had to be enforced in a localised manner, and the lack of large-scale uniform bureaucracy meant that had to proceed through local rulers. If you've ever had the (mis)fortune to deal with 2nd and 3rd world governments, you learn that there are laws, and there are interpretations of laws, and there is how Mr. X feels on a certain day. So the extent, implementation, and ferocity of persecution varied from region to region.
Thirdly, what was the goal of persecution? To a large extent persecution against Christians was motivated by a perception that rejection of Roman religious practice was culturally abhorrent, a form of anti-socialism that rejected a divine order and was politically seditious. Decius and Diocletian were somewhat successful in that they forced large numbers of Christians to sacrifice, or represent that they sacrificed, to the Roman gods and honoured the emperor. The goal of such persecutions was religious and social unity and peace, not extermination of Christianity as a sect per se.
Furthermore, by the time of these widespread persecutions, Christianity had become a significant minority, which is much more difficult to stamp out. To draw a historical comparison, if Communist China failed to eradicate indigenous Christianity, within the 20th century setting, is it so surprising that Roman era leaders failed in their own setting?
This answer is a combination of understanding history of persecution in the early church alongside Roman governmental systems. I have to head off right now but I can list some general reading on those two topics later.
What you have to understand is that Romans saw the gods differently then we do today. The did not care if you believe in them or not.
But they believed that it would anger the goods if you did not sacrifice to them.
So all they really wanted is to bring the christians to sacrifice, they did not have some ideological need to kill every christian. The romans often tried not to kill the christians, offering them deals like, how about you sacrifice to the emperor instead of the gods and all kind of thing like that. Many christians accepted these deals and they where fine.
However it seams that beeing a martyr in the arena was a way of showing how good a christian you are. That is why you had cases where christians would just volunteer for the arena.
Also I agree with the other post, the roman did not have the means to have large scale centrally directed persecution.