Penance (2022) ends with the La Sirena crew confronted by Confederate security. They raise their hands in surrender and Picard's hands are empty. When "Assimilation" picks up the very next moment, Picard is suddenly holding a phaser in his still-raised right hand.
As ICE enters the clinic and places Rios under arrest, Rios is wearing a medical lab coat with a stethoscope around his neck. The ICE agent turns Rios around and places him against the wall and cuffs him. His lab coat disappears between camera shots and the stethoscope is hanging off his shoulder.
Rios is arrested by ICE federal officers in an immigration raid at a medical clinic. At this time line, 2024, ICE has a strict policy against conducting such raids in areas deemed sensitive locations, a medical clinic is labeled as such. The officers must obtain permission to enter the clinic through the chain of command up to headquarters in Washington DC, and can only enter the clinic without permission under exigent circumstances involving national security or an imminent risk of death or violence.
When their ship comes out of the time warp around the Sun, the Earth is shown in the backdrop with a shadow in the northeast hemisphere. There should be no shadow as the Sun (viewer's viewpoint) is pointing directly head-on at it.
Picard met Guinan and became friends with her in 1893 in Time's Arrow, Part II (1992), yet in 2024 Guinan has no idea who he is.
During the psych eval, Renée Picard reveals a potentially career-ending vulnerability. No former test pilot / trainee astronaut would ever be so foolish as to do such a thing.