One tricky aspect of fast DSOs is that if the trigger circuit is running at full bandwidth, it may see ringing and ground bounce on a low-frequency square wave that the acquisition system is hiding from you at slow sweep speeds.
I'm not familiar with the TDS7404, but see if there's a lowpass filter option for the trigger (may be called 'HF REJECT' or something similar.) In general, try switching to a much faster timebase than you would ordinarily use, and see if you see a lot of ringing/undershoot appear. If there's an envelope or peak-detect acquisition mode, this may also give you a clue as to what the trigger circuit is actually doing.