The title says it all, when there's a error in my webpart I can't load the whole page.
I'd like just to don't display the webpart and still see the rest of the page and not just get the error page. Can this be done without catching all errors?
You have two options:
To elaborate on the first. It can be implemented using this pattern:
If you want to just remove the Web Part (or disable them all) you can add
to your querystring, then you can manage your Web Parts