Why does a DVR record the wrong program?

Two possibilities: 1) your clock is set slightly off. Clocks sometimes "drift" and you need to adjust their settings occasionally. 2) the networks sometimes screw around with the start and stop times of programs, to discourage people who "time shift" (record something to watch at a more convenient time). For example, this coming Tuesday, ABC has "Body of Proof" starting at 10:01, not at 10:00 - so if you record this show, you may miss the last minute of it.

Of course, "live" events like a football game can run overtime and affect the times of other programs on the same network.