How is Gertrude blind to her marriage to Claudius in Hamlet?

Gertrude does not seem to suspect any foul play in her former husband's death, nor does she seem to perceive any evil in Claudius's character. From the glimpses we receive of her relationship with Claudius, the two appear happily married, openly discussing Hamlet's alleged madness together and, from what Hamlet says anyway, enjoying a healthy sex life. She seems too enthralled with her new husband to even be willing to notice any defects in his character.
Of course, not everyone agrees with this interpretation. Some stagings of the play imply Gertrude might have been having an affair with Claudius even before Hamlet's father was murdered (hence, the two marrying less than two months after King Hamlet's funeral). Some even suggest she might have been complicit in his murder. It all depends on one's individual reading of the play or the interpretation of the cast and crew putting on the play for an audience.
Depending upon how the text is presented, Gertrude can also either come off as a guileless fool regarding Claudius's character throughout the whole play, not realizing until her poisoning that Claudius is a bad man, or she can be given some insight later on. Famously, Laurence Olivier's 1948 film version suggests Gertrude finally sees through Claudius's treachery in her last scene. Realizing Hamlet's drink has been poisoned, she consumes it first so her son will not be killed and so that the court will realize Claudius is a murderer and political schemer.