(Arcgis 10.2.1, JSAPI 3.8)
So, the main problem is that in my project when using tiled and dynamic layers the Tiled one is shown wrong. It's hard to explain but I'll try.
For my test case I add to my map one layer for all scales as Dynamic layer, and one layer for specific scales as Tiled map layer.
So when I zoom to map to one place and then toggle both layers I see that everything is OK. Then zoom to full map extent and once again to that previous scale but to different place (some kilometers from previous place) and then use map.centerAt() to get to that first place I get that strange behavior that Tiled map is shown some meters asside than Dynamic map layer.
Then zoom out and back in and once again its OK.
Please, tell me what could be the problem for that interesting behavior.
PS: coordinate system is WKID:3059