Wow, it's great. ^.^
There is nothing to correct tho.
I just want to make it more natural, because we don't say '그래, 잠 잘 시간이군.' often.
시간이 이렇게 늦은지 몰랐네 (Excellent)
그래, 잠 잘 시간이군 (Fine, but we don't say as often as korean subtitles do.)
-->그러네, 잠 잘 시간이네
-->그러게, 잠 잘 시간이네
잠자리에 들 준비를 하자고 (Excellent)