My dvr can only record two programs and will not let watch a 3rd program while taping two programs.?

This has to do with the number of "tuners" built in to your DVR. Most of the DVR's provided by cable/sat companies had only 2 tuners built in to them up until this last year or so. Basically - it means that your DVR can only tune to 2 stations (2 tuners) at once. So - if your recording 2 stations, there is not an available tuner to watch a 3rd. You normally can watch something from the saved list though since that doesnt require an additional tuner.

If you want to watch a 3rd program, you can either contact your provider for a newer DVR that may have more tuners (Dish now has the Hopper with 6 tuners, Direct TV has the Genie with 6 tuners, and many cable companies have their own versions with more tuners). Also - you could get another DVR like your current one and hook it up to another TV and record your shows on the other DVR. If you have whole-home DVR setup, you can stream those shows to your other TV later.

Watching a show live, or recording it, requires a tuner. Most DVRs only have 2 tuners.

Watching a pre-recorded show does not require a tuner, so you should be able to watch a show you already recorded while the DVR is actively recording 2 different shows.

Normally, most folks have so many recordings on their DVR they don't watch live TV anymore. Besides, you can't fast forward through the commercials with live TV.