Issues are no DC coupling, very limited input protection and limited range. Good luck using it for 5V logic, for example. Apart from the obvious issues like bandwidth (quite low for something like I2C or RS-232). Accuracy is usually quite poor (who cares about their volume drifting by a few dB, especially in consumer audio).
You can build an external attenuator (preferably variable, unlike the link you gave) with BNC connectors and circuit protection, but this will defeat the portable and cheap advantage. Especially by the time you bought a dedicated sound card. I wouldn't bother, but don't let that stop you from experimenting if you have plenty of time and no funds/space for a real (even used analog) scope.