Okay, so there's a number of problems with this normal map at the moment, most of which I think I know how to fix (the weapon isn't finished yet anyway). But there are two things that I don't know what to do about, both of them involving the normal detail being shown in reverse. They look like they might be related, but it's hard to tell.

Image showing problem here: http://img545.imageshack.us/img545/9360/oblivnormprob.jpg

As shown in the picture on the left, there are spots where the normal map suddenly appears to reverse direction, apparently in conjunction with an edge on the geometry.
Also visible in both screenshots, and indicated in the second, the little circular divot things are in reverse of what they are supposed to be. They are correctly oriented on the left side, incorrectly oriented on the right.

The relevant portion of the normal map is on the right, just for reference's sake. The blade is using "quadruple" symmetry, as in the blade is mirrored both on each flat side of the blade, with the symmetry there being the cutting edge; as well as "left to right" along the center of the flat of the blade.

Can someone clue me in as to what I need to do to fix this? I've done this sort of symmetry in other game engines (e.g. Unreal Engine 3) and not had a problem; I also know that Oblivion has items in the game that use this sort of technique (the steel shortsword, for example), and the method seems to work just fine there; why wouldn't it work here?

I may be wrong about this, but I think your problem lies exactly in the fact that the normal map is only a half of the blade, which means it has to be flipped over vertically. This results in the original dips to form bumps. You will have to re-map the model, so that you have the side of the blade as a whole. It is good to check original Oblivion textures and normal maps of similar items to see how they were made. Always remember the old modders wisdom - when in doubt check for references.

But that's precisely what I'm saying -- the Steel Shortsword model that already exists in Oblivion by default uses this exact same method for the blade textures, and it doesn't produce this kind of error. So what am I doing with this sword that's different from what Bethesda themselves did with the Steel Shortsword?

I took a look at all the steel and also the silver swords. The one you are mentioning does not have any decorative carvings on it's blade. The ones which do have carvings - Fine Steel and Silver Longsword or Claymores - all have their whole blade on the maps.

It's true that the Steel shortsword doesn't have "carvings" per se -- not the sort of curvy stylized artistic carvings that my sword or the other swords in the game have -- but there is still normal map detail on the steel shortsword's blade (e.g the fuller in the middle, and the general roughness/bumpiness).
That detail on the normal map is quadruply mirrored, just as on my own sword, and yet it doesn't result in this reversal problem. So clearly it can be done; but there's apparently some technical aspect to this that I'm missing. I don't see what I'm doing differently from what they did.

Could also be a problem with the NIf instead of the texture -- (ie. duplicate vertices, Flipped normals, etc.) - try opening the NIf in nifskope and running the various scripts on the mesh (ie. right click on the sword in the render window and run the various mesh options like Remove duplicate vertices, face normals, smooth normals, etc. ) and see if that clears any of it up.

And just like that, you solved my problem. (It was either "smooth normals" or "update tangent space" that fixed it, not sure which.) I didn't realize NifSkope could do stuff like that. Thanks!