In the photos Shawn took on the cell phone, Shangri-Lala's address is 1325 Beleveder Dr. Later when Shawn's talking to Lassiter and O'Hara, he says that Polexia "tends bar at Shangri-Lala's on State Street".
In the opening sequence, while the guys are watching TV early in the evening, looking out their window is a full moon low on the horizon. Since the Psych office overlooks the ocean it means it looks West, and with the moon rising in the East the moon shouldn't be visible from the Psych office until just before morning.
Juliet says that there will be a full moon that night, which is the third night in a row. This is scientifically impossible because as soon as the moon is full it begins waning.
The newspaper article that Stewart shows Shawn and Gus consists of six paragraphs that keep repeating.
In the flashback at the end, we see the killer smashing the Psych office window while standing next to it inside the office. In the reality at the beginning, Shawn and Gus wake up immediately after hearing the glass break. They would have caught the killer in the act if what was seen in the flashback actually happened that way.