How old is your 36? I have one of the no-dash models made back in '73. I love the gun but the front sight is at times almost impossible for me to see. I'm not sure why Smith put something on the gun with the approximate width of a razor blade but, that's what they did with the early 36s and I've learned to live with it.
When I first got the gun I shot everything consistently high. Several inches above my perceived POA. It took me a while to realize that it wasn't the gun nor was it the ammo that was doing it. The problem lay entirely in the way I lined up the sights. In order to be able to see the front sight I'd fallen into the habit of lifting the upper edge of the sight above the channel made by the fixed rear sight. Of course, that made me shoot high.
It took me a while to cure this habit. When I did, my gun shot perfectly well to POA.
Now, shooting left or right of perceived POA is another story. I've done that from time to time with my 36 and I've discovered that lighting plays a huge role in whether my shots are on target or go off to one side. Lighting from behind that hits my front sight unevenly will make the sight appear to be more to one side than the other. If I attempt to correct for that optical illusion I tend to place my shots in the direction that I've attempted to correct. For example: If there's back light that hits the right side of my front sight, it will appear to be further to the left than it really is. If I attempt to "correct" for that, I'll move my front sight to the right. The consequence is that I'll place all of my shots to the right.
Before I change my ammo, I'd try shooting the gun under different lighting. I'd also try shooting the gun off a rest or have a friend shoot it. The results may surprise you.