At the target and within the chain, TDI is always input and TDO is always output. TDI connects to TDO for chaining. But at the pod (FT2232) it seems common to label the pins with the name of the signal that they connect to. So the pod's TDO pin is an input for the signal from the target's TDO pin, and TDI is output to the target's TDI pin. This nomenclature is actually used in the FT2232...
Hi,
Do you have a scope at hand to verify the signals from the FT2232 where they reach the parts? Any type of overshoot especially on TCK can cause very strange symptoms. You might try a simple voltage divider made of resistors at the output of the ft2232 (3v3->2v5), a series resistor, or small parallel capacitance - and check if that changes anything...
Kolja.