When Max cuts the wire on the bomb, the timer starts to decrease rapidly, going down several minutes in just a couple of seconds. The bomb should have, therefore, blown up before he says "We may have a problem". Continuing on, Alex has the time to call Kara, and she has time to fly it into the air before it goes off.
When Kara hands over the papers to Olsen (just after the countdown speeds up) her hands are together in front of her in the side shot but by her sides immediately afterwards.
When Max cuts the wire on the bomb, the timer starts decreasing rapidly. Later when Kara is flying the bomb into the air, the timer has gone back to decreasing normally.
The character Maxwell Lord signs a paper on a clipboard presented to him by an underling. He appears to dot two i's to complete his signature. The name of the character contains no i's, but the name of the actor portraying him, Peter Facinelli, does.
Supergirl uses her laser-beam eyes to smash up the camera drone over National City, causing the debris to fall down... on the humanity below? She dives down to retrieve a bit of scrap she needs for further evaluation, but there is no concern for the rest of the (off-camera) spiraling wreckage that would potentially wreak havoc on the civilian populace.
The camera drone following Supergirl (Melissa Benoist) and then evading her as she pursues it, flies as if it is being piloted. By its very definition, drone, it couldn't have zigzagged through all the skyscrapers like that.
At 36:04 -sparks coming off Supergirl's boots.