There are a few major problems with finite fluids that DF manages to avoid.
First is the whole "map edge" problem. In DF, the map has fixed dimensions, and water sources that extend off the edge (rivers, oceans) are large enough that they can be assumed infinite. In Minecraft, the current 'map' is the group of chunks currently loaded, and bodies of water that extend off the edge can most definitely not be considered infinite. Imagine if, suddenly, your river spontaneously flooded (or, alternately, dried up) because you walked far enough away that the chunk the source was located on suddenly unloaded.
Second is the computational complexity of tracking water motion. Here, Minecraft and DF are quite similar - both have large, grid-based, 3D worlds. But in DF, the game can gracefully account for higher processor demands via FPS reduction. Minecraft doesn't have that luxury; reducing the game clock to account for extra processor demands just isn't viable.
The third problem is the issue of non-even division. Consider a 'blob' of DF water, say four full blocks of 7-deep water. That's 28 water units. Now, imagine this water is poured into a 3x3 room (perhaps to form a cleansing pool or something). 27 blocks spread out evenly to form a 3-deep pool, while the one extra unit of water effectively 'skips' around the room. In DF, this is only visible if you've got depth numbers enabled or are actively studying the pool, and even then it doesn't seem weird - at most, it looks like waves. This kind of issue would be really, really ugly in Minecraft, though, where you could see this one, thin 'slice' of water dancing around atop the surface, perpetually looking for a spot it can settle into. A more realistic solution (namely, using floating points to correctly calculate the water's depth) would be incredibly complicated.
Now, granted, there are ways to work around some of these problems. I assume the modders who have implemented finite water have taken a stab at some simple workarounds. Sufficiently-deep water (perhaps a 3x3x3 cube?) could be assumed 'infinite', for instance. But the computational challenges alone make implementing finite fluids pretty much impractical.