Reading through this...
In the circumstances, I don't find anyone particularly remiss.
The McCann group took around 10 minutes to register that she really had gone and to organise a quick local search. When she was obviously nowhere to be found, Matt went to the reception. The receptionist set the missing child protocol in motion (which must have taken a bit of time to get through to those responsible and to provide any further info). The police were called roughly 1/2 hour later when the initial OC team couldn't find her either.
Up until then, people were just hoping that she'd wandered off on her own, or if she had been abducted, she could have been dumped alive nearby, but might also be in a potentially dangerous situation, e.g., fallen into the swimming pool, a ditch, had been run over or whatever else.
If there are only one or two patrols in Lagos at that time of year and night (it wasn't yet the summer season), then organising a local search as a priority seems to make sense to me. In context, it must have been a frantic 20-30 minutes, with people with strange accents in a state of anxiety trying to communicate.
To OC's credit, the protocol was implemented very quickly with numerous people out searching. I'm not convinced that ringing 112 in the initial minutes would be a natural reaction in a foreign country with a receptionist who knew where they lived, understood English, could get a search party togther and ring the police on their behalf.