Like many others, I read about this unpleasant scam whereby someone has paid for the Google Adword “Firefox” to the extent that Firefox searches show their link (which pretends to be Mozilla’s site) in the results:
I couldn’t say that this is Google’s fault, it seems more that one of their customers is acting dishonestly – what responsibility they have for that I do not know. However, this is exactly the kind of thing that leads me to object to the Omnibox in the Chrome browser. I think it’s fine that the location bar allows you to use shortcuts to search, but combining the location bar and the search box seems to me to be an unwelcome development. The search provider is disintermediating the location, presenting an opportunity to hijack the user to the highest bidder.
And as this example so vividly demonstrates, it is locations that we can trust, not search terms.
From Åkerö 
Report it! http://www.mozilla.com/en-US/legal/fraud-report/index.html
Searches using Firefox’s search bar or the Chrome omnibar NEVER show advertisements, and can’t be hijacked by the “highest bidder”. If you search exclusively from a search bar (or omnibar) you’ll never see those ads.
I don’t know how you came to the conclusion that Chrome displays ads in it’s in-bar search results and Firefox does not, when both clearly do not with a simple test.
Except that, when one finds a trick to get high search rankings, even though it will only last for 1 day before Google finds out about it and manages to fix it, you will gain a spot right into the user’s browser’s ‘smart’ address bar, with all its opportunities for phishing.
I must say I agree that I feel the address bar should just search in my local bookmarks and history. That way, when I enter e.g. my bank’s name I can be sure that I get there, and not at whatever page happens to rank highest in Google. After all, always going to your bank’s site through your bookmarks is I think universally considered the safest way to get there.
And let’s not pretend that Google’s ranking system can’t be gamed — that’s like saying Wikipedia’s words always ring true.
This specific issue is by the way another good example why it is not good practice to let people show one URL in the link content but to have another underneath it. In this case doubly so, as the actual link is also obfustcated because of the click redirect. Short URL services as popular now on Twitter have an equal problem. Basically, it removes the ability to see where you’re going, and even worse, tricks you into thinking you’re going somewhere else. This always irks me about Google’s ad links. Well, at least they don’t do *that* in the user’s address bar, too.
Here’s a better place to report, since Google controls AdWords and not Mozilla:
https://services.google.com/inquiry/aw_tmcomplaint
Oops, should probably mention that link is for trademark HOLDERS (ie Mozilla) not just anymore.