Should I 'admit' a weakness of a paper even if it's 'obvious'? Example: I have a simulation to run that requires social media data sets. The data sets that actually matter are too big to be able to simulate anything useful on. Instead, I picked a data set that's much smaller that had similar properties and I (hoped) would therefore have similar behavior.

One thing I discovered was that different data sets, even when they're of a similar size, can behave radically different in ways that I'm not exactly able to predict from those properties.

Obviously this is a major weakness of the paper, because now I don't have a way to even guarantee that those 'similar properties' even matter anymore.
I wonder if your research is ready for prime time. Not getting consistent results and not knowing why is a fault. Maybe you should continue work for a bit. 

But for the question itself, it is better that any shortcomings come from you rather than from someone else. 

At a minimum, you have an interesting "future research" section to write. Maybe you should find a way to look at the larger data sets or others that will give you better insight into what is really going on.