Ranked in these QuestionsQuestion Ranking
Pro Very simple to use
Corona SDK is completely free as of March 2, 2015. That includes pro-tier plugins.
Pro Lua syntax
Uses the great and easy-to-learn Lua programming language.
Pro Good documentation and lots of tutorials
Pro Well supported
Pro Cross-platform desktop and mobile
Corona works on OS X, Windows and Android (including Kindle Fire & Nook).
Pro Ability to call any native (C/C++/Obj-C/Java) library
Pro Amazing learning curve
Corona does not throw photoshop-like madness full of buttons editor. You can go as fast as you want, learning and building game from ground up. Eventually, you'll learn how much corona is doing for you. But to start you don't have to master complex editor software. It's a great tool to learn to start game development if you want to learn how to program and make games. Your experience will be 100% transferable to any other Pro game engine.
Pro Great community
Pro Corona Simulator
Corona SDK ships with Corona Simulator, which runs your game/app directly on your PC/Mac and updates every time you make changes.
It provides immediate feedback to your actions, you can see your changes right on the screen, without necessity to make build to device. Getting instant feedback really boosts tenfold prototyping and development speed.
Pro Very comprehensive API
It's very quick to get things up and running with Corona SDK. The API is extensive and while it's not 100% feature-complete with the iOS API, it's close enough that you could create tons of games and never run into a roadblock.
The API docs can be found here.
Pro Content scaling
It's easy to create a game that looks good on many different sized mobile devices.
Con Making a device build requires internet connection
To build your app for the device (iOS/Android/AppleTV) Corona requires to fetch resources from online. This would include base application template and plugins. This allows not to perform local build or use Xcode or Android Studio to do a build. Even Large games/apps would build very fast with good internet connection.
Your code never leaves computed. Corona SDK would transfer some information to determine which plugins and pieces has to be transferred in order to make a final steps in build.
As a bonus - you get basically one button press to get from your Corona Simulator game to game on a device.
Con Closed source
Since you don't have access to the code, you can't make changes to the SDK. You even have to implement workarounds on issues that have long been reported, but never fixed.