It sounds like one of the first reported problems with the series 3 TiVo is that the infrared sensor might not work if you have a plasma/LCD TV and set the TiVo close to the TV's own sensor. People are saying it'll require a hardware change to fix and one enterprising owner has already done that on his own (here are the full instructions).
I have a plasma and a series 3, but the TiVo is in a lower cabinet about 8 feet away from the TV, which is mounted back up on a wall. I get great remote coverage, easily out performing the Comcast DVR it replaced. From reading the tivocommunity thread, It's unclear if this is due to certain models, backlights, or just faulty hardware.
If you're running into these issues, be sure to check out the thread on it. [thanks for the tip Wook]