I think you’ve pretty much zeroed in on the problem by yourself: the issue is that ‘Date’ is being supplied as the value of the tribe-bar-date URL query (when that piece of text is converted to a date it is ultimately interpreted as something like 1st January 1970).
Of course, this should really be a valid date or should simply be empty. Sometimes though a plugin – or more often a theme – uses something called a polyfiller (typically a piece of JavaScript) attempts to convert our placeholder text into an actual input field value to achieve better cross-browser support. If this happens, though, then it also needs to basically undo its changes before a form submission takes place. In this case, it may be that final act of cleaning up isn’t happening.
To confirm this theory can you try deactivating all other plugins and switching to a default, unmodified theme – then see if the same thing happens? If it does not, try reactivating each plugin / your theme, one-at-a-time. This might help to isolate the conflict, if indeed there is one.