Dragon Age Inquisition is a big game so there's understandably some problems affecting Thedas at this point and while BioWare will hopefully fix them soon, here are some common problems with the PC version and how to fix them.
A lot of Frostbite 3 games lock their frame rate at 30fps, which can lead to ugly stuttering issues. To get around this, you'll need a PC which can handle 60fps, but if you do create a desktop shortcut to your DA:I executable (which will have been created during installation), find the "Target" field and add the following with the quotation marks “-GameTime.MaxSimFps 60 -GameTime.ForceSimRate 60+”
Should your character become stuck in the opening cutscene, either restart the game or use the aforementioned frame rate unlock.
Your game may be experiencing DirectX issues, and if that's the case, reinstall or update DirectX, and try searching for any Windows updates. If neither of those work, try downloading the Visual C++ Redistributable for Visual Studio 2012 Update 4.
Invalid game license issues can be fixed by repairing the installation through Origin, or by reinstalling the game. If the game won't start, and you meet the minimum system requirements, try updating or re-installing your various .Net Frameworks. This issue can also be caused by using a GeForce card on an Intel processor, and the easiest solution here is to try downloading the latest GeForce drivers.
You can find details of these fixes and more on CrashWiki.com.