With Chrome I occassionally run into problems. For example, there was a time when I couldn't get my Amazon cart to work with Chrome. I popped open IE and it just worked. My bank used to not work with Chrome, but now does. I recently had a site where the links in the sidebar weren't clickable, but I know I had clicked them before. Went to IE and it worked.

Printing is also really hit or miss. Weird font sizes, or sometimes blank areas. Not browsing proper, but still worth mentioning.

Admittedly this doesn't happen often, but enough for me to notice.