Spoilers, but really just annoying stuff not plot stuff:
a) FL is a police officer. She's been a police officer for ~3-4 ish years, because one of her first cases is the one that indirectly leads to her brother's death.
b) hinted about earlier, but really made a big deal about starting episode 12? or so, she's like "yes, I went to the US, but I came back to be a police officer and avenge my brother's death. and they KEEP TALKING ABOUT THAT.

YOU WERE ALREADY A POLICE OFFICER. YOU NEVER WENT TO THE US. Unless she went as a kid? between the judo stuff and becoming a police officer and then came back, to avenge his death before he was actually dead? (I suspect that there must have been some sort of plot/timeline change midway through authoring, because also he was only in jail for like a year, assuming I'm doing my math right.) But she was ALREADY A COP. She sat and talked WITH HER (alive) BROTHER in her cop gear about what an amazing profiler Nam Han Joon was and how she wanted to meet him.

Other people have raised valid points about chemistry and such, but I was just enjoying it even so, it but then the timeline went crazy and wrong and inconsistent and so now I'm just cranky (okay I just ignore the part where they keep dwelling on the timeline.)