People may criticize the psychiatrist's scene, but it's actually completely necessary. The audience may have figured everything out the minute they saw Mrs. Bates' corpse, but the characters are still clueless.
The fact that it's a private investigator looking for Marion instead of the police (in which case her interactions with the Highway Patrol Officer and California Charlie would've come to light) becomes this once one remembers that the 40,000 dollarsnote Around $338,000 in 2018 money, adjusted for inflation. Marion stole was all undeclared income. Involving the police would've alerted the Intimidating Revenue Service.
And Lila when she thinks Sam was working with Marion, immediately says that they don't want to press charges as long as she returns the money.
With the Word of God that Marion was planning to go back and return everything, it makes sense that she might not fear the police - since she was there when Cassidy said he didn't declare it.
In the shot that pulls back from Marion's eye, it is possible to see her throat moving just slightly. Presumably this was simply because Janet Leigh couldn't remain totally still during the rather complicated shot, but if one likes, there is a more chilling interpretation: that Marion, while mortally wounded, wasn't quite dead yet and wouldn't be until she was put in the car and drowned in the swamp.
This is doubly so in the fourth film of the series, which is a flashback to before the events of the first film: Norma thinks she murdered someone by strangling them. Norman uses the woman's car to hide the crime (similar to how he would later do to Marion). Unfortunately, Norma didn't kill the woman. So, it is possible that Norma hadn't completely killed people before.
Norman goes through the motions of cleaning up after "Mother's" murder of Marion with the demeanor of having done this before. And indeed, when the psychiatrist refers to the unsolved disappearance of two local girls, we realize that he has.