1. If you paste into a textarea, the newlines get silently stripped when you submit the form.
Documented here: http://code.google.com/p/chromium/issues/detail?id=104620
But it's more insidious than in that example, because you never find out the newline-stripped version got submitted.
I've sent some embarrassing emails where everything was smashed together into a single block of text.
2. Double-clicking a submit button submits the form twice. Firefox does this too, so I guess it's my app's fault for not handling the duplicate submissions properly, but Safari gets this right.
3. DNS pre-fetching. Make sure it's off before testing your move to a new webhost! http://blog.chromium.org/2008/09/dns-prefetching-or-pre-resolving.html