Take a look at this question on SuperUser. Apparently, it was migrated from ServerFault, and was originally asked by user 3d1l. However, now look at the API result: http://api.superuser.com/1.0/questions/91137 (Warning - This will start a keyless request limit, as I've not included an API key). This returns...

{
  "total": 1,
  "page": 1,
  "pagesize": 30,
  "questions": [
    {
      "tags": [
        "windows-vista",
        "wireless",
        "network",
        "connections"
      ],
      "answer_count": 2,
      "favorite_count": 0,
      "migrated": {
        "new_question_id": 98620,
        "to_site": {
          "name": "Server Fault",
          "logo_url": "http://sstatic.net/serverfault/img/logo.png",
          "api_endpoint": "http://api.serverfault.com",
          "site_url": "http://serverfault.com",
          "description": "Q&A for system administrators and IT professionals",
          "icon_url": "http://sstatic.net/serverfault/apple-touch-icon.png",
          "state": "normal",
          "styling": {
            "link_color": "#10456A",
            "tag_foreground_color": "#444444",
            "tag_background_color": "#F3F1D9"
          }
        },
        "on_date": 1262620840
      },
      "question_timeline_url": "/questions/91137/timeline",
      "question_comments_url": "/questions/91137/comments",
      "question_answers_url": "/questions/91137/answers",
      "question_id": 91137,
      "creation_date": 1262308465,
      "last_activity_date": 1279463955,
      "up_vote_count": 0,
      "down_vote_count": 0,
      "view_count": 254,
      "score": 0,
      "community_owned": false,
      "title": "How to completely remove a wireless network setup from vista?"
    }
  ]
}

There are two oddities here. The migration data claims it was migrated, but says "to_site" was ServerFault. Surely this should be "from_site"; similarly the new_question_id should similarly be old_question_id).

More annoyingly, there is no data on who asked the question. Are we supposed to spin up a separate request to the origin site to request the user data? If so, it would be much more convenient to list at least the name of the question poster, as very often one just wants to display the username associated with the question.