In the final scene with Shawn and Juliet, Juliet's hand position on the couch changes back and forth several times between shots.
There are no papers in Little Rock, AR called the Observer or Daily Herald.
After Juliet kicks him out, Shawn is unable to find anywhere to stay except with Woody. However, Shawn has been shown sleeping in the Psych office multiple times and the office has also been shown to have everything Shawn would need to stay for at least a short time.
As Shawn is messing with his phone, trying to recall his home phone number (555-0135), Gus spits it out and states that it's part of the Fibonacci sequence. While this is technically true, it's not all in sequence (as some numbers are skipped)...the sequence is 0, 1, 1, 2, 3, 5 and on from there.
A professional and experienced grifter/identity thief would know not to carry all of their fake ID's with them. For one it is an obvious indication of who/what they are if anyone sees them and if the ID's are seen by a police officer it gives the police probable cause to arrest them as having multiple drivers licenses from different states is illegal.