There are a few different was to approach error logging in an open source BIRT report. This is an example of how you can use log4j and a custom class to generate log4j output using a try/catch block in JavaScript.
importPackage(Packages.com.opentext.birt.logger);
logger = new BIRTLogger("initialize", "BIRT Logging Example.rptdesign");
try {
addalert("something");
}catch(ex){
logger.logError(ex);
}