I would like to point out a couple of oddities or inconsistencies in the plot of Lolita. One is that Lolita does not get pregnant during all the time she is living with Humbert Humbert and obviously engaging heavily in sex. Humbert makes no mention of doing anything about birth control. It just seems like a question Nabokov chooses to avoid dealing with, although there are many indications that he must have had the risk of pregnancy on his mind. Somewhere in the book Humbert says that he would like to have "a whole litter of Lolitas." And then when Humbert finally meets her again, she has become pregnant. Her pregnancy leads to her death in childbirth, and her death expedites the postumous publication of Humbert's confession.

It also seems a little implausible that Lolita would know where to address a letter to Humbert after both of them have been moving around by themselves for several years.

It is difficult to assess if there are any logical inconsistencies in Nabokov's work.  Part of the reason that this is difficult is because nothing is direct and straightforward in Nabokov's work.  This is by design, something that Nabokov wanted.  In order to be able to assess if there are any plot inconsistencies, one has to start from firm ground in making such assertions.  Humbert's narrative is so unreliable and so filled with "swimming colors" that little is clear from it:  

"...what makes Lolita something more than either a case study of sexual perversion or pornographic titillation is the truly shocking fact that Humbert Humbert is a genius who, through the power of his artistry, actually persuades the reader that his memoir is a love story." 

Humbert's success in persuasion makes much of the plot logically consistent and logically inconsistent.  Whether or not Qulity would follow them across the country for something that he apparently does with many girls can be seen as logically inconsistent.  Whether or not Quilty is an "extreme version" of Humbert further helps to add inconsistency to the plot of the story.  In the end, the logical inconsistencies that present themselves are reflections of a narrative that, itself, is far from certain.