I use Google's Blogger service to create this blog. One of Blogger's features is the ability to moderate comments. In order to see the comments, however, you have to click on an arrow next to the comment, and it drops down to reveal the full comment. This works in all my browsers except for Google Chrome. In Chrome, clicking has no effect. I have to open Firefox or IE in order to moderate comments.
Another example is iGoogle. All these third-party gadgets work fine, but the Google Calendar gadget doesn't work at all. I see only a giant error message saying that the URL is too "large." (See the screenshot above.)
Yet another example: For months, some percentage of my Google Alerts messages were being unceremoniously dumped into the Gmail "Spam" folder, as if Google was concerned that Google was a spammer. To fix the problem, I had to create a Filter in Gmail and tell it to "Never send it to spam" when I get e-mail from Google Alerts.
There are probably other examples in my own experience that I can't recall for the moment. What about for you? Have you noticed Google stuff not working well with other Google stuff?