(1) Add a feature that gives the option to redirect Bundle error messages to
either a tooltip, or a new document .
(2) Add a feature that allows you to click on a Bundle error message, and
see it automatically jump to the offending line in the original document.
(i.e. error message at line 700). This could be done by providing an error
parser regex (perhaps bundle specific), so if the error regex matches, it
grabs the line number from the error output, and jumps to that specific line
number in the original document, making it easier to edit the document!

These features are already in TextMate. You can edit the bundle to redirect error messages to a file (if it is a shell command use 2</dev/null, etc). Unfortunately it isn't as easy as it could be to redirect stderr to a different place than stdout (like the output dropdown in the bundle editor) so this may not be feasible for you.

For number 2, the PHP bundle does it when you press validate and it detects an error. You can take a look at that bundle to see how they do it. The command is Validate (ctrl+shift+v) and it goes to the first line with an error.

Brandon