I've tried 0,300 and 300,0.  I can't seem to get a true offset no matter what.  For this dimension was pulled and 0,300 given in an ortho direction as an offset, and you can see that it ended up at 254 and change.

You're not giving it a distance from the source [after all, a dimension line can often be a different distance from the two definition points, so which should it use?].  Rather, you are giving it a location for the dimension line.  If you just type in a number by itself, that location will be at the distance you call for in the direction of the cursor location from the last-picked point in the process, which latter will vary depending on the type of Dimension, whether you gave it two points to dimension between or used the select-object option, etc.

I find in experimenting that it doesn't even honor ORTHO mode relative to the last point in locating that position, which disappointed me.  But if you're doing horizontal/vertical Dimensions and by giving it two points to dimension between, you can get the location you want relative to your second point by typing in @300,0 or @0,300 [sometimes with minus sign on the 300] or @300<0 [or other angle as appropriate].

I'm having a problem with offsetting dims from source.  When I pull a dim line on an object and I type an offset distance I get random distances every time.  For instance, I dimension an object, and enter 300mm as a distance for the dim line from source, and I end up with a dim line that's anything but 300mm from source.  The distance is always random, and its always close to the value I enter but off by 50-150mm.

Any help would be greatly appreciated!