In one scene where Tommy asks to ride David's horse, Alice can be seen clearing off the table, only to have the dirty dishes reappear a few seconds later.
While David and Alice are arguing in the restaurant, the plate on the tray Alice is holding shifts from one side of the tray to the other and back again between shots.
When the alarm clock goes off, Alice knocks it to the second shelf (at around 1h 35 mins). Alice goes back to sleep and some short time later, without either her or Tommy having moved in the bed, the alarm clock has returned to the top shelf of the nightstand.
When Flo loudly introduces Alice to all the diners, a camera cut shows Flo waiting on a table while she is still speaking.
When Alice and Tommy first see the "Leaving New Mexico" sign, the traffic light they are approaching turns from green to yellow. Following a very brief exchange inside the still-moving car, the light is then shown to be green, and they go right through the intersection without having slowed or stopped. There was no time for the light to have gone through a full cycle.
Tommy says the A7 chord hurts his fingers. A7 is one of the easiest chords, even for beginners. Kristofferson would know this and could have asked the script be altered, and recommend a more difficult chord.
As Alice is opening Mel's Diner in the morning, she turns the sign over to "open", then proceeds to put dirty dishes away. While it's typical that the dishes would have been picked up and cleaned the night before, not all establishments adhere to this process.
The piano Alice plays for the audition is an upright piano, but the sound is of an electric piano.
Opening scene, supposedly Socorro, New Mexico, shows palm trees, eucalyptus, and an orange tree - much too cold a climate for these.
Alice is supposedly heading to Monterey, but when she leaves Phoenix, she goes to Tucson, which is in the opposite direction.
Driving from New Jersey to Monterrey, California, there is no reason to be as far south as Arizona. The most likely route would be taking Interstate 80 all the way from New Jersey. which enters California north of Lake Tahoe, then transferring to southbound Interstate 5 in Sacramento.