I have checked a bunch of RSS readers and haven't found one these meet these three requirements:
1- Show a continuous list of articles with their subjects in a single view. This way I can quickly scan them and decide which ones I want to open and read. I don't want to touch each feed and view its articles. I subscribe to tens of feeds. Don't show any feeds which do not have unread articles. I don't want a list of feeds with a count. This is useless for me if I can't see the article subjects.
2- Be able to mark as read, only the ones that showed on the screen or mark by touching an article and it marks that article and upward to the beginning of the list. This feature was on a WP7 reader and it was very handy. All the Android readers I saw have the 'Mark All As Read' option and it marks all of the articles including the ones I haven't seen yet. Not useful.
3- Integrates and syncs with Google Reader. I read the same feeds on my iPad.