The Acclaim can't display 720p video anyway, so if you did get 720p (or higher) content to it, it would have to downsample anyway. And that would require either the site to work harder (which it won't, since it's free+ad supported) or the phone to work harder, which means a faster battery drain with no benefit to you watching. So the YouTube app probably fetches the highest quality video it can play (or possibly the lowest).

 

Android's YouTube application is afforded two different formats, a standard definition and a higher quality one. If a video is not playing correctly, I would suspect that it's conenctivity issues or a link to a video that can not be played on the device because it has not been transcoded to a format for mobile (yet). This may happen with newer videos.