I know some intact dogs who are perfectly restrained about marking, you wouldn't even know they were intact... and some who are OBSESSED with marking, it's all they want to do! If I had a dog of the latter persuasion, I'd probably neuter them. Some dogs literally seem driven insane by the urge to mark - drooling, licking, marking every surface even if they only have a drop left. Maybe because they've never been able to breed and are frustrated, or because they were never given restrictions or guidance to teach them where and when it's ok to mark. Idk but some intact dogs are really gross about it, while most aren't.
I would put a belly band on him and clean the spots REALLY well. Maybe get a professional carpet cleaner if you have carpet. You can use a blacklight to find pee. I'd do this whether you plan on neutering him or not, and supervise him all of the time!!! Tether him to you or crate him if necessary!