The puzzles. At first, it may seem like an ordinary child's hobby; however, vampire lore holds that vampires (and other supernatural creatures) cannot resist puzzles or riddles.
An even more disturbing possibility...what if the immortal monster that "turned" Eli comes back, finds her with Oskar, and gets the idea to repeat history?
Jossed by the author, who subsequently wrote a short-story sequel which reveals that Eli turned Oskar herself.
The teenage pimp may have been able to guess that Hakan was a pedophile because Hakan was looking around in a shifty manner that indicated he knew the place was a relatively well-known child prostitute pick up area, but why on earth did he constantly bug Hakan about the prospect of spending money on a child prostitute at a public library?
Public libraries are surprisingly good places for shady dealings. No one thinks it's weird for two people to be talking quietly, almost everyone who goes there has a task that they'll be focusing too intently on to think about eavesdropping, and it's still a well-lit, public place full of witnesses if things go badly enough that they might get violent.
Also Håkan was looking around in a way that probably made the pimp guess he was there for that reason.
The ending has some serious Fridge Horror for some viewers. Many people see the end of the movie as sweet, since the child protagonist ends up together with the child-vampire friend (and possible romantic interest). The Fridge Horror comes from realizing that the creepy pedophile that had been caring for the vampire up to that point started out exactly the same way, and much of the plot was the vampire manipulating events to get rid of a servant who could no longer handle his duties — which means that in fifty years, the protagonist will be the old creepy pedophile, and the cycle continues...
Still horrific, but in a different way, is how this is handled in the source material. Her helper is actually just a guy she met when he was already old... while he was observing children on a jungle gym. This could be seen as a good thing though, as she may not treat the new friend as poorly.
The Americanized version, Let Me In, restructures some of the scenes and dialog to hint more strongly that this is in fact what's going on, though the question is still left open.
It's possible that Eli could "turn" Oskar, but that opens up another closet full of Fridge Horror...
There is also the possibility that Oskar doesn't help Eli out by murdering people. He doesn't kill the guy who woke Eli up, and also is quite shocked when he learns that Eli lives off the rings and money of the people she and her helpers murder. There is a pretty big difference between offing a complete stranger and hitting a bully on the side of the head.
In particular, the interpretation that Oskar is going to become Eli's new guardian... which directly implies that, since Eli is Really 700 Years Old, that Håkan could easily have been in the same position as Oskar was at one point. On the DVD commentary, John Ajvide Lindqvist says that he likes that the movie is ambiguous on this matter, but that it was not the story he intended when he wrote the book.
Also, Eli assures Oskar that she didn't steal money from people she's killed. She claims people gave it to her. How a pretty but androgynous 12-year old waif gets money from strangers is not explained. In the book, Håkan is a pedophile and that explains his attraction and devotion to Eli. So, the theme is still subversion to darkness or vices, but in a different way. Håkan represents the darkness associated with the fact of who Eli has to be to survive, while Oskar represents the light. Eli is more than fine with stringing Håkan along to get what she needs, and Håkan is a much more morally repugnant figure with less to pity than portrayed in the movie.
An easily overlooked detail in the original movie half explains this. One of the toys in Eli's apartment is a silver and gold Faberge puzzle egg. So presumably she has been hording wealth for centuries. Now where she got it in the first place....
