If you don't know NewRelic, you should stop reading it and visit their website. New Relic is the best tool for software application active-analysis that every company should pay for.
New Relic can log your application errors with all information about it (headers, request parameters, error response) including error type, error date and time and even counting how many times an error occur between some time space.
Also, NewRelic measures how your application performs: how many secs your app taken to response a given request.
NewRelic has a great Profiling tool which can describe by method call level, which method is consuming more time/resource to be done, request by request. This is a huge help to find software implementation problems and also, to check if your submission in fact solve it later.
It also has Alerts to e-mail you (or your team) if your application goes offline or starting to error more than your configured Threshold.
Everything can be configured; but if you doesn't know how to, you can use their defaults which is great, too.
NewRelic support is awesome. Well trained people with great support by e-mail, phone or even conference call (depending on your plan).
If you have your application deployed on Heroku, I advise you to contact NewRelic team for price negotiations. Otherwise, you may expense more than expected with NewRelic by its price per dyno.