How will google look on this? Say, a website's about sport, but its one page is about airlines. How will google's ad looks at that page?
The fact your site is about sport but you have a page about airlines should not make a difference. As long as your keywords are highly relevant to your landing page you should achieve a good quality score.
Google's ads reflect whatever is on the page, what the website viewer has been looking for on Google, and what ads are available in their country. First Google's Adwords bot will crawl the site - this might take 10 mins to a few hours - so at first your ads might be about sport or misc - then after Google adbot has crawled - they should be about airplanes. Hope this helps mate
In other words, if i get 40 cents for a click at my sport pages i'll go on to get 40 cents at that airline page too. Am i right?