Episode #4.7 - S4-E7
Stupidity: It is stated that the police got the fingerprints of the culprit thanks to a certain object. In other words, they investigated the murder without taking any fingerprints from any suspect - even the one who has been jailed for shooting the corpse - and they even had his file already from the previous inquiries.
Episode #4.6 - S4-E6
Stupidity: This is another episode when with a very limited number of suspects, not checking the phone records makes the case more complicated than it would be, but more importantly, the bad guy keeps the phone used for the shady affairs constantly switched on for no reason. No attempt is made by the police to trace the area it comes from, either - in fact it's very naive of the Commissioner to even try to call the number - but it works.
Episode #4.6 - S4-E6
Stupidity: The police finds a message the victim recorded on the phone. Conveniently, there is no timestamp on the message; it's a vital clue and with a modicum of effort surely a date of the recorded file could have been determined - but of course it would have made the mystery easier.
Episode #4.2 - S4-E2
Stupidity: The way the investigation proceeds makes no sense - it is especially obvious for us viewers having actually seen the scene; Karl arrives and meets the wife of the victim, who is busy in the kitchen. He walks just a few feet outside, placing his doctor bag on the bench that is right there, and again, right there with no wait, he pulls a deck of cards out of his pants and puts that on the table. A gunshot is instantly heard. Karl and Katie Peters should be perfectly able to validate each other's alibi, because there's no way that either of them could have shot the victim.in the shack in the less than 10 seconds they lost sight of each other. Instead, the whole episode goes on as if it could be possible for everyone to just go on and shoot someone while being mere meters away from each other.
Answer: Most likely they had only tropical exotic drinks, he wanted an old fashioned English beer.