MacBook Air: Playing 1080p vs 720p videos
Your MacBook Air supports the following resolutions at 16:10 aspect ratio:


1440 x 900 (native)
1280 x 800
1152 x 720
1024 x 640 


It also supports the following at 4:3 aspect ratio:


1024 x 768
800 x 600


Since 1080p is technically a resolution of 1920 x 1080 your MacBook Air isn't going to display a 1080p movie at its best on its built in display. However, your MacBook Air does support an external resolution of up to 2560 x 1600 pixels, so you'd be able to take advantage of 1080p in that scenario.

Finally, whether you download 1080p or 720p movies also gets down to personal preference. Most people I know with true HD TVs still only download 720p versions because the difference to them (especially while watching most movies) is negligible. Basically, do you notice the extra pixels during a high speed chase in an action movie or not? Many people don't, some people do.

In summary, if you're downloading movies only to watch on your MacBook Air via it's built in display, there's no real advantage to downloading the 1080p version.