When Barry is in "Flashtime" he is using a pen to write on a glass screen. The pen's ink would simply not flow fast enough to allow him to use it. further to this, he drops the pen and it appears to fall at normal speed, instead of appearing to fall in slow motion as one would expect. Even if the pen had been brought into the flashtime state to allow him to use it (though no suggestion is ever made he can do this with inanimate objects) the pen would have still fallen at the rate determined by gravitational pull (9.81 m/s^2).
Near episode's end, Caitlin tells Harry that when her alter ego is control of her body, she doesn't know what Killer Frost says and does. But in "When Harry Met Harry... (2017)", she mentions to Barry that Killer Frost once attended the Burning Man festival; if Caitlin's personality is suppressed that much when Killer Frost emerges, that's a memory she shouldn't have.
Despite already being in Flashtime, Jesse runs off at super speed to retrieve Jay. She should only be able to casually jog away since she is already running in super speed.
Although this is a superhero show, it generally tries to follow the laws of physics. In this case, though, from the time the button was pressed until the bomb went off would have been less than 5 nanoseconds. Barry made the one-way trip between Star Labs and the hangar 4 times, so he would have to travel at nearly 5000 times the speed of light to accomplish this feat, even if the two facilities were next door to each other.