On most Tektronix digital scopes there are two settings for the time base. One is what they usually label as "equivalent time" and the other is "real time".
The real time mode is just that, it takes all samples in a single sweep at the specified sampling rate and directly displays the values captured.
Using equivalent time (puke!) the waveform is built from
multiple sampling sweeps, with each sweep offset (via adjustment of the input delay) from the others by a small amount.
The equivalent time mode is fine if your looking at general waveform shape of repetitive (say a clock) signals and you are not concerned with glitches, spikes, and other random features. However for looking at non-repetitive signals or looking at/for spikes, glitches, ringing, etc., it suxors!
Regarding the query on the probe and hook-up, there are two issues, noise and frequency response. Your described setup for what you were looking at would take care of most of the noise issues, but if you were trying to look at edge rates, high frequency glitches or noise, and other critters of the high frequency world it wouldn't give you accurate data
FYI... you could have used a 100mv/div setting and used the vertical offset to look at the signals with DC coupling and still had ~5mV accuracy. (Also, you can use the zoom functions of Tex scopes to adjust the
displayed waveform area of interest to full screen size.)