Use browser.manage().logs().get('browser')
browser.manage().logs().get('browser').then(function(browserLogs) {
// browserLogs is an array of objects with level and message fields
browserLogs.forEach(function(log){
if (log.level.value > 900) { // it's an error log
console.log('Browser console error!');
console.log(log.message);
}
});
});