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This answer to How far off did Apollo 11 land? mentions that:

Eagle was already 3 miles downrange from the expected position at the start of descent, due to residual pressure in the docking tunnel pushing the spacecraft apart when they undocked.

How was this estimated? (is there a source, or is this just a generally accepted value)

Guidance systems has inertial sensors and a computers, but this is a tricky part, one spacecraft becomes two independent spacecraft. Was the delta-v from the push unaccounted for because it happened before the lander's guidance system's accelerometers were activated? Was there any way this could have been noticed by Doppler shift from Earth and the computer's information updated? Was it corrected-for?

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    $\begingroup$ The 3-mile long figure was initially estimated by the LM crew seeing surface landmarks three seconds earlier than their cue cards told them to expect to; they were going just about a mile a second during that phase. $\endgroup$
    – Russell Borogove
    Jul 20, 2019 at 23:30
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    $\begingroup$ See the annotated transcript starting at 102:36:11. hq.nasa.gov/alsj/a11/a11.landing.html $\endgroup$
    – Russell Borogove
    Jul 20, 2019 at 23:38

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According to the mission report, immediately after separation, there was disagreement on the LM's velocity between its primary guidance/navigation system and its abort guidance system:

The undocking action imparted a velocity to the lunar module of 0.4 ft/sec, as measured by the lunar module primary guidance system. The abort guidance system disagreed with the primary system by approximately 0.2 ft/sec, which is well within the preflight limit. The velocity was nulled, assuming the primary system to be correct.

That section (4.9 UNDOCKING AND SEPARATION) says nothing about the docking tunnel. A check with the sextant on the LM showed an alignment error greater than expected, but within tolerable levels.

Earlier in the mission there were some perturbations in the lunar orbit, and the tunnel is given as one possible cause:

Several unanticipated problems severely affected navigation accuracy.

[...]

The third problem area was the large number of trajectory perturba­tion in revolutions 11 through 13 because of uncoupled attitude maneuvers, such as hot firing tests of the lunar module thrusters, undocking impulse, station-keeping activity, sublimator operation and possibly tunnel and cabin venting. The net effect of these perturbations was a sizeable down­ range miss.

section 7.8

The is the only reference in the mission report regarding the effects of the tunnel on trajectory.

Though plausible, I'm not convinced that the docking tunnel pressure was a significant factor in undocking. It's not mentioned at all regarding undocking, and barely mentioned as a possible factor during orbit.

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