You need to understand that all digital televison sets are 1080p ready. That does not mean that they actually display 1080p. They scale 480i, 480p, 720p, 1080i, or 1080p to their native pixel densities. For TV content, this is OK. For a computer monitor, it is likely to look like crap.
You need to set the external monitor of your Mac to the native resolution of your TV. That is 1680 x 1050. My guess is that your TV can display only 30 Hz, but a setting of 60 Hz may work.