After doing some research on it, >>this here<< seems to be the most likely issue. Now while this guide talks about it appearing while generating Pokemon, it actually applies to some Pokemon you caught normally in Gen 3 as well. I don't know the exact mechanics behind it, nor will I do further research on it to try to understand it, but apparently when you transfer Pokemon from Generation 3 to Generation 4, sometimes a portion of the bytes gets converted into those 'trash bytes'. From what I gather it seems to come from combinations in terms of OT name, name of the Pokemon and a few internal values you won't see anyways.
Now I don't know how close this actually is to the real reason why that Jirachi won't get transferred over, but it does seem to be at least a possible solution.
Now I don't know how close this actually is to the real reason why that Jirachi won't get transferred over, but it does seem to be at least a possible solution.