That's a good point, but I think things were more nuanced than that (at least IIRC ;)...I haven't re-listened to it since the original broadcast)...the victim's disappearance was not thought of as a disappearance until at least a week or so later -- her body wasn't found until a month later. Even though her family reported her as missing the day of her actual disappearance...I believe Adnan claimed that he thought she had just gone on some crazy trip, as teenagers are wont to do. Sure, the victim's family would argue that she was the kind of good girl who would never do such a thing, but she was also someone who carried out a sexual relation with Adnan without her family's knowledge or acceptance...so, your typical -- but complicated -- teenage drama, except that it ended in a tragic and mysterious murder case. But if Adnan is innocent, his excuse makes sense to me -- he knew what a rebellious girl Hae Min Lee was, and there was no reason to keep frozen in mind the day of her initial disappearance.
That said, it did bother me how he apparently never thought to call on her during the time of her disappearance, even though they were no longer a couple. That was probably one of the strongest pieces of circumstantial evidence against him, in my eyes.
One of the most compelling aspects of the case for me is that while I can see why Adnan garnered the sympathy of advocates and the interest of Serial's producers, at least enough to warrant a full season of coverage...I still couldn't quite shake the feeling that even if he isn't guilty beyond a reasonable doubt...that he might still be guilty of the actual murder. I can't remember the last time a story so full of ambiguity so completely captured my attention.