A simple way to distinguish between SignalTap internal acquisition and JTAG signal integrity problems is to press the "Read Data" button and transmit the same acquisition again. If you get arbitrary different waveforms on each re-transmit, it's a signal integrity problem. If the waveform is exactly kept, the garbage is already in the internal stored data.
I can't however imagine a way to get toggling data from a (1.) registered and (2.) known static signal, except for an aquisition clock that violates the minimum pulse width specification, e.g. caused by a too high PLL frequency or the PLL falling out of lock.
JTAG signal integrity problems can be easily brought by EMI, particularly power electronic devices switching near by, possibly also by on board cross talk of fast signals. Unfortunately, SignalTap data streams are apparently transmitted without any checksum or CRC.