When a tip of the day contains a hyperlink, the link is selected by default; when there's no link, "Show tips on startup" checkbox is default-selected. For the latter case, simply pressing Enter closes the dialog; for the former, on Windows, it seems to press, while on Linux, it's reported to open the tip in the browser (erAck).
While the different behaviour of controls is a bug of its own, this specific issue is about the need to explicitly pre-select OK in the Tip of the Day dialog (or arguably "Show tips on startup"), for consistent behaviour, without unintended effects on keypress.
We should always focus on the Ok button.
*** This bug has been marked as a duplicate of bug 125871 ***