Did the Portuguese police make mistakes in the process of the investigation? I'm sure they did, but this does not make them totally incompetent. Especially given the location - a small coastal resort in Portugal. If you look at UK major investigations there have been mistakes but perhaps of a different nature. For example, in the Soham murders in a rural village there were mistakes made by the local police including I believe a slow response time in putting out an alert.
Anyway, if the UK police were in charge of this investigation they would I assume suspect the McCanns at some stage. Likely straight away to eliminate them from the inquiry. Seems to me the Portuguese had not go to that stage yet and when the new lead detective took over the case it was something of a fresh start and then the investigation had a chance to review and progress as evidence/logic/procedure dictates. A good opportunity imo for innocent parents to offer every assistance. If the tapas 7 were warned that this was just an attempt to build a case against them or the McCanns rather then possible elimination I can understand their trepidation. Perhaps the McCanns did try to cooperate at this stage and offer every assistance. Something else that seriously hampered this case was the media here and in Portugal imo.