There are two types of logs, telemetry logs and dataflash logs.
Everything that shows up in the ‘MAVLink Inspector’ in QGC is saved to a telemetry log on the receiving computer.
The dataflash logs are saved to the Pixhawk SD card.
Both types of log can be analyzed using MAVExplorer.py.
If you need to do some real-time analysis there are some mavproxy features for that, or you can use the Widgets->Analyze feature in QGroundControl.
Let me know where you want to start looking and I can get more specific.
-Jacob