The Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933), in Siman 271 (Se’if Katan 5; listen to audio recording for precise citation), writes that when a person recites Kiddush for his family and other people at the table, he must have in mind that they will be fulfilling their Misva through his recitation. They, too, must have in mind to fulfill their obligation by listening to his recitation of Kiddush. Therefore, the Mishna Berura advises the one reciting Kiddush to first announce to the family and the others at the table that they must pay attention to the Kiddush and have in mind to fulfill their obligation. It occasionally happens that people at the table are daydreaming or otherwise inattentive during Kiddush. In order for them to fulfill their Misva, they must listen attentively to each word of Kiddush and have in mind that they satisfy their requirement by listening to the recitation of Kiddush.
Is it preferable for each individual to personally recite Kiddush, or for one person to recite Kiddush on behalf of all the others?
There is a general Halachic principle of "Misva Bo Yoter Mi’bi’shluho," which means that it is preferable to fulfill a Misva personally, rather than designate an agent to do so on one’s behalf. This rule, however, applies only to personal Misvot, that are not done collectively. For example, it is preferable to personally betroth a woman for marriage (Kiddushin) than to appoint an agent to betroth her on one’s behalf, even though betrothal is effective through an agent. When it comes to Misvot like Kiddush, however, which many people can perform collectively, we employ the rule of "Be’rob Am Hadrat Melech," which means that a public performance of a Misva brings greater honor to the Almighty. This is the consensus among the Halachic authorities, as mentioned by the Mishna Berura on numerous occasions. It is thus preferable for one person to recite Kiddush on behalf of everyone present, and individuals should not insist on reciting their own Kiddush. Of course, if the person who recites Kiddush does not project in a manner that allows everyone to hear each word, or if he mumbles or mispronounces words, or does not have in mind for everyone at the table to fulfill their Misva, then certainly others at the table should recite Kiddush in order to fulfill the Misva. If a person in such a case does not have a cup of wine, he may recite the Kiddush along with the person reciting for the group, having in mind that he recites Kiddush over the wine that he will later take or that will be passed to him.
Hacham Ovadia Yosef, in his work Yabia Omer (vol. 6, Siman 11), rules that an Ashkenazi may fulfill his Kiddush obligation by listening to the recitation of a Sepharadi, and, conversely, a Sepharadi may fulfill his obligation by listening to the Kiddush of an Ashkenazi. As long as the person reciting the Kiddush recites each word properly, and the one listening hears each word, and they both have in mind to fulfill the Misva, the obligation is fulfilled, regardless of whether Kiddush was recited in Ashkenazic or Sephardic pronunciation.
Summary: When one person recites Kiddush on behalf of others, he and they must have in mind that the listeners fulfill the Misva through his recitation. It is preferable for one person to recite Kiddush on behalf of others, rather than for each person to recite Kiddush independently. A Sepharadi may recite Kiddush for an Ashkenazi, and vice versa.