Archer jabs a syringe of morphine into Lana's right thigh, while a closeup view shows a shoulder and a jacket flap lapel. There are no lapels on Lana's pants.
When Archer is ordering room service, his sawed-off shotgun can be seen in a holster on his right hip. In the next scene, it is no longer on his leg.
Beer freezes at a little above -3°C, so all those bottles in the cooler full of dry ice should have long since exploded.
No chemical reaction occurs between carbon dioxide and water, at least not if you just add and mix them. The effect shown is physical and far weaker than even a genuine deflagration, let alone an explosion.
When Lana and Archer are riding the air boat, they are sitting middle to low of the fan; when the boat sinks, however, the seats are closer to the top when it goes down.