After questioning Reggie, as Beckett takes off her disguise, she undoes the top button of her shirt. In the next shot, her shirt is fully buttoned up. Later, it is shown undone again.
At the beginning, when the (probable) murder weapon is found, it's a revolver, described as a "cheap street piece." Beckett notes that the barrel is threaded for a silencer, but it is physically impossible to silence a revolver, since blow-by between the cylinder and barrel creates almost as much noise as the barrel report.
When Beckett comes out of the pool, a hotel employee gives her a pool skirt. When she swings it around her hips, water droplets fly out of the skirt meaning that it was already wet. That means it wasn't the first take and Stana had to put it on multiple times before.
The closeup shot of Beckett picking a lock shows a lock pick and tension tool inserted into a lock and, after being gently shaken, the door pops open with ease. When picking a lock, you still need to rotate the cylinder (usually at least 90°) the same as you would when using a key. Picks don't make doors just magically open.