How can I view the contents of the Minimongo database in the client with Meteor?

You can either use a server-side privileged admin solutions like Houston or any other MongoDB admin interface.

If you want to query data on the client for a quick inspection, you can use console.table:

console.table(Tasks.find().fetch())

Mongol does this, FTW, thanks to Max Savin.

Also I noticed no one has mentioned it but there is also for chrome a 'Meteor DevTools' extension that you can add to chrome tools. Once your meteor project is running you can see in chrome tool a tab called 'Meteor' that will show you what MiniMongo has.