Dogberry's a goofy, ignorant, and disregarded character.
I believe Dogberry is an uneducated and overlooked character but has pure intentions. When he found out about Don John and Borachio's wrong doings, he did everything he could to put make them face the consequences of their actions. He may have two different intentions the primary one is that he want the respect of other, but he also wants to be looked at as heroic. Dogberry said, "One word, sir: our watch, sir, have indeed comprehended two auspicious persons, and we would have them this morning examined before your worship." This line shows that he isn't the brightest but he means well.
I think for the most part dogberry is a static character. One of the only small changes he makes is his opinion on Borachio and Don John. Dogberry said, " Write down, that they hope they serve God: and write God first; for God defend but God should go before such villains! Masters, it is proved already that you are little better than false knaves; and it will go near to be thought so shortly."
I believe the plot is, Claudio returns from war and quickly falls in love with Hero. Claudio and Hero pledge their love to one another and decide to be married. But Don John has decided to disrupt everyone’s happiness. He has his companion Borachio make love to Margaret, at Hero’s window and he brings Don Pedro and Claudio to watch. Hero by suddenly accusing by Claudio of her wrong doings on the day of their wedding and abandoned her at the altar. Hero’s family members decide to pretend that she died. That night the watchmen overhear Borachio bragging about his crime. Dogberry and Verges, the heads of the local police, ultimately arrest both Borachio and Conrad, another of Don John’s followers. Claudio decides to marry hero's cousin which is actually hero. When Hero reveals herself as the masked woman, Claudio is overwhelmed with joy. Benedick then asks Beatrice if she will marry him. I think dogberry effected this plot in a huge way because if he wasn't around or didn't do the things he did, Hero's reputation would have been ruined, Claudio and Hero would not have been married, and Don John would not have been arrested. He also effects the theme by basically getting Hero and Claudio back together.