Hello Pavel Kornilov,
I have gone through the example and the problem is lod not the API 3.3 .I have taken the example and commented the lod and the application is working fine.Only problem is lods. you can check this http://jsfiddle.net/U8VxC/. for the example you have mention.
Also similar issue with http://help.arcgis.com/en/webapi/javascript/arcgis/samples/map_customtilelevels/index.html sample.
Though it has only one basemap.
Hello Matt Lane ,
I believe both the layer configuration are different and you are right watershedlayer is configured for 13 levels [0-12] and publicSafetyLayer is configured 17 levels [0-16].So i guess one one layer exceed another layers level gives the problem.check the service layers where the level information is elaborated.