I run a free product without a revenue model as well. (DuckieTV, a chrome extension / node-webkit app, http://schizoduckie.github.io/DuckieTV )

I have zero costs though, since it's serverless and all hosted on Google and Github's infrastructure.

For privacy reasons I have made the deliberate choice to not include any log reporting tools or use any tracking services that could possibly make development a whole lot easier.

Thankfully I get some support from a couple of other people that mostly help with small dev tweaks and supporting users, finding out what goes wrong and providing excellent feedback.

I can really recommend setting up a subreddit so that people can help themselves and others, and you can provide some feedback where needed.

All in all the load of user support has been quite easily manageable, though now with Trakt.TV's debacle with the new API there is definite pressure to fix things.