For the purpose of recording some scenario on my screen in 720 HD format, I would like to set the window of a particular application to the exact size of 1280x720 pixels. With some patience, I managed to resize it manually to the required size. Is there a better way to achieve this? I am on MountainLion.
As far as I'm aware, there is no inbuilt functionality in Mountain Lion to do this.
I use an application called SizeUp which allows you to do what you're asking. Here is part of the preferences dialog:
It's also handy for stretching windows fullscreen, unlike the green icon on the top left of each window, which behaves differently per app!