Mixxx uses the BPMDetect class from the SoundTouch library for BPM Detection. There is also another opensource library called BPMDj which is harder to use but is more accurate.
I personally wouldn't rely on either though. Then again I am a hobbyist DJ so I tend to rely more on my ears.
EDIT
There is a much better OSS library called aubio. It can also do beat detection and onset detection.
ANOTHER EDIT
Mixxx has now moved onto the VAMP Plugins set, which is much better, supports aubio and many other beat detection libraries. It also supports key detection and other audio analysis features.
