It could be a couple of different things.
First, read over THIS THREAD and make sure your system is up to recommended specs.
If your system is fine, then a little further down in that same thread are instructions to clear your browser's cache and the Flash cache. Do both of those. Every time the WGT introduces an update, you should clear both of your caches. Sometimes older files that are stored on your computer are incompatible with the newer updated files.
If you're still having issues, you might need to update your video card drivers. If you're like me, you also need to close everything but the actual game window and play on the lowest quality settings.
Oh and also, there is no penalty for swinging through the shot. Usually the next swing is much smoother too.
Good Luck