As far Chrome's shortcomings, I have only come across two. The first is that the back button doesn't remember your position in the previous document. So if I click on a link halfway through an article then click back Chrome displays the top of the page.
The second is the initial page, with snippets of recently browsed pages, isn't quite as Terminal Services friendly as about:blank (my homepage in Internet Explorer).
Despite these two shortcomings it's an excellent browser. Uniquely positioned to take advantage of the coming multicore revolution since each tab gets rendered by a separate process that can run on a separate core.