The first thing you have to do with the river birch is make sure is a river birch and not a paper birch. This is pretty easy thing to do if you know what to look for. The paper birch has a white trunk. The river birch on the other hand has a multicolored trunk in most cases with a tint of light orange in it. They also tend to be much rougher and have lots of bark peeling away unlike a paper birch.
The river birch is for most part a very healthy tree. The only two known diseases that river birch carry are anthracnose leaf blight and iron chlorosis. The anthracnose is very rare but iron chlorosis is a very serious problem that when left untreated will kill the tree in less than a growing season.
Iron chlorosis is so prevalent in river birch because we have taken them from there natural habitat (the river bottoms) and tried to put them in our yards. Now their look really nice and they do not get all the diseases that paper birch get but the soils in your yard are far from what this tree wants. It prefers soggy, nutrient rich soil and most residential yards have gritty sandy soil. So the problem is with your soil and as you can guess if you have iron chlorosis you have a problem with iron. The soils get leached of iron and that higher's the PH in the soil or in other words takes acid out of the soil. You tree needs that lower PH soil to survive.
One of the most harmful pests in river birch are japanese beetles. These insects will gang up on river birch trees and eat every last leaf on the tree. You can learn more about japanese beetles at the japanese beetle page.
Here are some things to look for in River Birch:
Yellowing in leaves in spring or summer (very serious)