"I didn't notice him left the room" is grammatically impossible: we can't have two conjugated verbs in the one clause. Your conjugated verb is the past tense 'didn't notice' so the verb 'leave' has to be in either a gerund or bare infinitive form: it cannot be in the past. "I didn't notice him leaving the room" and "I didn't notice him leaving the room" are both correct. There is a slight difference between them. The infinitive suggests that you saw the completed action, while the gerund suggests that you saw the action in progress. For example, "I noticed him leaving the room" might mean that you saw him get up and walk towards the door, while the "I noticed him leave the room" would make it clear that you knew that he had left the room. However, they are very close in meaning, and could be used interchangeably in this case. I hope that helps.

"I didn't notice him leave the room." and "I didn't notice him leaving the room." are both correct

I see. Thank you

Apologies for the typo in my response: I obviously meant to say this: "I didn't notice him leave the room" and "I didn't notice him leaving the room" are both correct.

You're welcome! Keep up the good work!