What is more accurate , the fozgometer or the diplay of the oscilloscoop

Azimuth adjustment makes very little difference to channel balance.  Azimuth adjustment is done to minimize crosstalk.  In so doing, one can target ether of two goals: (1) Equal crosstalk, L to R and R to L, or (2) Minimal crosstalk without regard to whether the db of crosstalk is equal, L to R and R to L.  Both goals are valid.  But you can almost never achieve both of these possible goals at the same time with the same cartridge.

From your verbal description, I am not sure what it is you were measuring, output from each channel or crosstalk.

You can do a quick visual check first by dropping the stylus on a mirror. The mirror doubles the visible angle, making it easier to see with the naked eye. I would still recommend that you go further than a physical inspection. Sometimes the stylus isn't mounted exactly perpendicular to the top of the cart body. You can't see that when you do a visual inspection.

You really don't need the fozgometer or a scope to set azimuth. A DMM will work just as well. But is has to be a really good one like a Fluke. If you do use a scope, keep in mind that they vary in quality. If you're not sure how good your scope is, trust the fozgometer or the DMM. 

Also, if you don't have an azimuth adjustment, just leave it alone. Shimming the cart can do more harm than good.

If you use the mirror method you should get a mirror that is surface silvered like that from a 35 mm  slr camera, or your image will be way off.  The foz always works for me but a new battery should be used every time. I agree re: shimming the cartridge...much too crude adjustments for tilt, and cartidge will not be mounted solidly enough.

Neither........Do the adjustment by ear!

http://www.whatsbestforum.com/showthread.php?9097-Azimuth-adjustment-the-easy-way

Doing it by ear sounds like a good idea, but I would only do it as a last resort. First, it requires a fair amount of experience and practice to get good at it. Its far easier and faster for someone who's never done it before to just use a DMM. As long as the DMM is a quality unit, it will be more accurate than going by ear. There's no guesswork involved. When you're done, you know its right.

There's other factors to consider as well. The article you reference talks about tuning the room to compensate for the azimuth being off. Again, at first glance it sounds like a good idea, but its not. When room tuning is brought up, the first thing you usually think about is tuning the room vs eq/processing. There's a downside to using an eq because you're fooling with the signal in ways that can have a big effect on SQ. There's no downside to adjusting the azimuth directly. If its off, adjusting it will always be a positive thing. If you choose to leave the azimuth alone and use an indirect method of adjustment, you now have 2 problems. First, if the azimuth is off due to the stylus not being perpendicular to the top of the cart body, you still have the crosstalk. Fooling with external factors to get a center image can't eliminate the crosstalk, so its only a partial fix. Second, what do you do if you have more than one source? If you play a CD, now that's going to be off because you made proprietary adjustments meant for your TT only. When you make changes to your room, they apply to all sources, not just one.