Mini-DVI is video only.
Your resolution should be equal to the MacBook's display. If what you are seeing is blurry, you are probably not using a correct adapter, and may be using composite video or S-video. Both will look horrible on an HDTV.
Use this adapter, or one like it:
You will also need a separate audio cable that connects your MacBook's audio output to whatever audio inputs your HDTV uses... maybe something like this, but check your connections to be sure:
First we need to know which one of the 9 different models of MacBook you have. To see which model you have go to the Apple in the upper left corner and select About This Mac, then click on More Info (and then System Report if you’re running 10.8 Mountain Lion). When System Profiler comes up check the Model Identifier and post it back here.
The Late 2009 model 6,1 has a Mini DisplayPort.
The Mid 2009 model 5,2 has a Mini-DVI port.
If you connect the MacBook using a Mini DVI or Mini DisplayPort to HDMI adapter you will probably need to use external speakers or a 3.5mm stereo headphone jack to RCA sound plugs connected to a stereo sound system if your TV doesn't have separate RCA input plugs or a 3.5mm stereo input plug for audio with the HDMI plug. The Mini DisplayPort to HDMI doesn't carry audio unless you have the Mid 2010 model 7,1 and there're no audio plugs on most TVs to work with HDMI since it's expecting audio with the HDMI. But check your TV manual to see if it has audio plugs that work with one of the HDMI ports.
If you have the Late 2009 model 6,1 White Unibody with the Mini DisplayPort rather than the Mini-DVI there is an adapter that uses the Mini DisplayPort and a USB port to combine video and audio to HDMI. It's only 2 channel stereo not 5.1 Dolby Surround.