When Alan sits down on the arm of the couch, his sister Kathy puts her left hand on the couch arm near his leg. On the very next cut, she now has her left hand holding his wrist.
When Jane throws the money at Blake as he gets ready to make a call, he has his left hand hanging down by his side. On the next cut, his left hand is in his pocket.
Jane tells Alan that the $790 she has spent represents about one tenth of a percent of the money in the satchel. Since they thought they had $100,000 (later determined by Danny the blackmailer to be $60,000). One tenth of a percent of 100,000 would be $100, so she spent closer to eight tenths of a percent of what she thought they had. A tenth of a percent of $60,000 would be $60, and $790 would be slightly over 13 per cent of that amount. So, in any case, the screenwriter was bad at math.
The entrance door of Alan and Jane Palmer's apartment does not have a peephole. However, most residential apartments have a peephole; therefore, the apartment was probably either built on a sound stage or is an office made to look like an apartment.
Since she fell off the balcony backwards, she would have landed face down, due to the rotation of the fall.
Jane tells Danny they're going to Coldwater Canyon, but moments later they turn into the Bel-Air Estates, which is miles to the west of Coldwater Canyon (which doesn't even intersect with Sunset Blvd., which Danny notes they've just turned off). However, in one possibly longer version of the film, she tells him they're going to Coldwater Canyon on a second meeting, which happens minutes later, with other scenes in between.
When Don Blanchard was trying to get Lt. Breach to dredge the lake looking for the body of Alan Palmer, he could have offered as evidence that Jane Palmer held a gun on him, took the claim check, then knocked him out, all which could be corroborated by Kathy Palmer, and also that Jane was working with an accomplice that he saw coming out of her apartment. As Lt. Breach said they only act on a missing persons report "...if there's some evidence of foul play..", this should have been enough evidence that Jane was caught up in criminal activity to warrant dredging the lake.
After Jane's first attempt to kill Danny on the trip to the hills, she goes to the beach and abandons her car. She then walks to the ocean and throws something into the surf. The assumption is that it's her husband's gun (but she possibly tossed his wallet or some papers that she took out when leaving the car). Yet Jane has the gun at several points later in the movie.
Kathy, Jane's sister-in-law, is a single woman, yet she is wearing a fashionable blouse that buttons up the back when she searches the Palmer's apartment after her brother disappears. Though she could have used a zipper hook helper instead of assistance from another person.