Yeah the game has occasional frame rate issues, i don't know why though, but i read somewhere that the game is actually pushing it higher than 60fps and that's why it occasionally gets messed up. Hopefully it will eventually be patched, for me this is not something game breaking and it does not happen all the time, but we all experience different things with different severity.
Last gen CoD games are not true 720p, they are upscaled. I also read somewhere that the native 1080p only applies to the single player but i could be wrong here. It doesn't really make a difference if the game is natively 720p or 1080p because most people will never know the difference. You need a huge TV or need to use a video projector, and be relatively close to the screen to actually see a difference.