When we see Barney behind Diane in the gas station shop at the beginning of the movie he is wearing his cast-arm-sling ruse, yet when he tells the story to Jeff as they drive along we see that when he meets Diane he is not wearing that at all.
When Jeff starts writing the note to Diane that he's going to look for her, he puts no dash after "Di". Yet when you see him put the note on the windshield, there is now a dash after Di, and the handwriting is different.
(at around 9 mins) Barney is in his car, parked, facing downhill on the north side of Pine St., between Pike Place and 1st Ave. at the Pike Place Public Market. As he sees the attractive woman approaching up the hill toward him, he exits the car, approaches her and asks her where the post office is. She tells him it is a mile "up" and off of Hanley. From their location, up the hill to 1st. ave., drive two more blocks east to 3rd ave., turn right to the south, proceed two blocks south and at the intersection, on the south east corner is the post office.
There is no post office in Seattle "off of "Hanley St."
In the beginning of the film, when Barney is meeting his daughter at the bus/train station, as the bus pulls up, the camera angle widens and you can see the extras ("background") waiting at the top of the stairs for their cue to walk down. As the scene progresses, the woman in the jeans and red sweater and her male companion are seen coming down the stairs as Barney and his daughter begin to walk up the stairs.
When Barney goes to Jeff's apartment there's a nice artistic touch...the reflection of his face in the outside car mirror as he gets out of the car. The problem is that in order to make that shot work the mirror had to be aimed at the sky...making it useless when driving.
The goof item below may give away important plot points.
Towards the end of the film when Rita is struggling with Barney, she escapes by using the car cigarette lighter to ignite his handkerchief (which he later says had chloroform on it). Only problem is that chloroform is non-flammable. If it had been ether then yes, boom-bang, but he clearly says it was chloroform.