The main factor that predicted completing the full vaccine sequence was knowing, at the first visit, how many shots were needed. Gardasil is ideally given as three shots over the course of 6 months, where the second and third shots are given 2 months and 6 months after the first shot. (This varies slightly for Cervarix.) On the face of it, this totally makes sense. Of course women are more likely to come back for the second and third shots if they know they need them. However, I tend to believe that the fact that, over the course of the study, only 50 percent of women completed the full vaccine series suggests a more serious issue with how doctors convey information about the vaccine to their patients... or how they don't.
That said, I'm not certain that my normal willingness to believe that doctors are doing a bad job talking about sex is actually supported by the data in this particular instance. Most of the girls in the study reported that their doctors did talk to them about the need to get more shots when they received their vaccine, and only a slightly smaller fraction came out of that conversation still unaware of the number of needed shots. It's possible that some of the lack of follow-up was actually more related to other issues - such as problems with transportation or failure to pre-schedule appointments - that weren't captured by the survey. This seems particularly likely as the group at largest risk of failing to complete the vaccine series was young women between the ages of 16 and 20. Whereas older women are likely to be highly motivated to complete the series if they've started it, and younger women are likely to be largely steered by their parents, that middle group is at an awkward age where they might get pushed into the first dose by convention and then forget to stay on top of the planning.
In addition, there was also one interesting side note I wanted to mention. For some reason, bruising after the shot was associated with a decreased likelihood of finishing the vaccine series, but pain was not. In reality, this is probably an artifact of low survey participation, but it still makes me come up with some hypotheses for this strange discrepancy that could be best summed up as, "Oh, teenagers.... they have the strangest priorities."