Note: I present here some information defending Millikan, but please note that I do not necessarily agree with the article it came from.
From the feature article "In Defense of Robert Andrews Millikan" by David Goodstein (American Scientist, January-February 2001):
Awkwardly, an examination of Millikan's private laboratory notebooks indicates that he did not in fact include every droplet for which he recorded data. He published the results of measurements on just 58 drops, whereas the notebooks reveal that he studied some 175 drops in the period between November 11th, 1911 and April 16th, 1912. In a classic case of cooking, the accusation goes, he reported results that supported his own hypothesis of the smallest unit of charge and discarded those contrary results that would have supported Ehrenhaft's position. And, to make matters very much worse, he lied about it. Millikan's 1913 paper contains this explicit assertion: "It is to be remarked, too, that this is not a selected group of drops, but represents all the drops experimented upon during 60 consecutive days, during which time the apparatus was taken down several times and set up anew." (Emphasis in the original). Thus, Millikan is accused of cheating and then compounding his cheating by lying about it in one of the most important scientific papers of the 20th century.
The author defends some of Millikan's actions.
[...] More than one of the entries in his notebooks show the result of a computation and then the comment "very low something wrong," perhaps with an indication of what Millikan thought might have disturbed the measurement. Needless to say, such entries were not included in the 58 drops Millikan published.
At first glance, this procedure certainly appears questionable. But one needs to dig deeper. The notebooks also contain a calculation with the comment "This is almost exactly right, the best one I ever had!!!" And yet Millikan did not include this drop either in his crucial 1913 paper. These discarded measurements, the good and the bad, were all part of a warm-up period during which Millikan gradually refined his apparatus and technique, in order to make the best determination possible of the unit of electric charge. The first observation that passed muster and made it into print was taken on February 13th, 1912, and all of the published data were taken between then and April 16th. This period of roughly two months is what Millikan refers to when he talks about "60 consecutive days," although the interval was actually a bit longer (63 days), in part because 1912 was a leap year.
During these nine weeks Millikan recorded in his notebooks measurements on roughly 100 separate drops. Of these, about 25 series are obviously aborted during the run, and so cannot be counted as complete data sets. Of the remaining 75 or so, he chose 58 for publication. Millikan's standards for acceptability were exacting. If a drop was too small, it was excessively affected by Brownian motion, or at least by inaccuracy in Stokes's law for the viscous force of air. If it was too large, it would fall too rapidly for accurate measurement. He also preferred to have a drop capture an ion a number of times in the course of observation, so that he could investigate changes as well as total charge, which had to be an integer multiple of the fundamental unit, e.
[...] He had no special bias in choosing which drops to discard: Allan Franklin of the University of Colorado reanalyzed Millikan's raw data in 1981 and discovered that his final value for e and for its margin of error would barely have changed had he made use of all the data he had, rather than just the 58 drops he selected.
There is actually much more to this than what I quoted. The article contains the complete story.