You have picked an excellent act to talk about the character of Claudio in this play. Claudio is presented as young and earnest, a warrior who has accomplished "in the figure of a lamb the feats of a lion" during battle. Now, in peacetime, he is looking for a bride worthy of the fame he has already worked hard to achieve. Critics seem divided about his character. When he sees Hero, it is only after establishing that she is of a good family and has money that he announces his intention to woo her to Don Pedro. Such actions suggest that Hero is nothing but a trophy to Claudio--a fitting beautiful bride for an ambitious young man eager to make his way in society.
Unfortunately, the action in this important scene does not give us much leverage to argue differently about his character. In spite of the light-hearted jesting with Benedick about his radically changed character, when Don John enters with news of Hero's infidelity, Claudio, in spite of his recent protestations of love, is quick to believe the worst of Hero. He doesn't contradict Don John's words in any way, in spite of the obvious malevolence of his character, and both Claudio and Don Pedro play right into the hands of Don John like innocent and naive flies buzzing ever closer towards the spider's web.