The tool recommended by Flutter is Sentry. I've tried it and it's perfect for me. First you check out the tutorial about it.

Report errors to a service
How to keep track of errors that users encounter.

What does it look like?

With Sentry, whenever an exception occurs, it'll report it to Sentry along with the stack trace, device details... Then you can check out all the issues that got reported on a nice dashboard.

As you can see, you'll see how many times an error happened, and the graph shows you when it happened, so you can roughly estimate whether it still occurs or not.

On Flutter Web

The configuration to make it work correctly for the Web is a bit more complex than for Android and iOS. See my previous blog post about it: http://blog.wafrat.com/setting-up-sentry-for-flutter-web/.