It's not SiteAdvisor which checks a site's digital certificate but your browser.
Sometimes a certificate problem will lead to a site failing to load in the browser; sometimes you just get a dialog window asking if you want to proceed even though the identity of the site cannot be verified.
If a browser warns about a website because of a problem with the site's certificate then you have two options : either you override the warning and proceed to the site or you back off. It all depends on how serious are the potential risks involved in going to that particular website. For instance, if the browser warning says that your online banking website has a digital certificate which was not issued to the bank then I would say you should exit, fast. If it's a site you go to just to browse, it might be okay to ignore a warning like that.
If the certificate warning blocks access to the site altogether (which it might in Firefox, for instance) you can modify some of the browser settings to turn off that sort of warning. Me, I see those warnings and I respect them. I'm not going to compromise my browser security just because a site owner can't be bothered to make sure his site's digital security certificate is valid and up to date.
All this is generic advice about certificate warnings. I'd need to see a screenshot of any actual warning to see which browser was issuing it and what it meant.