Difficult if there are issues where a child is concerned, differing views on parenting and boundaries could be pretty fundamental to the happiness of all three of you and any potential future plans. Your child is vitally important in this.
As for things like tidiness, could you compromise? You can of course look at compromising on niggles like this generally ie you give more on one issue, he gives more on another...
I have to say I'm almost dreading this in a future relationship as my ex had so many issues, he was a bit ocd on aspects of cleaning and such as well and other things which I still have a complex about now. I've vowed not to let another man make me feel less of a person because of his issues but easier said than done.
At the end of the day, relationships take working at and compromise but not to the extreme at it's too one sided. Is he worth trying to work through the issues?
Have you discussed any of this with him?
As others have said, it's only been 5 months and there is no rush to get serious with each other. To be nearer doesn't have to mean moving in together, you could just move closer.