Yeah, Mike shows up - sort of - in The Cat Who Walks Through Walls - some other characters from The Moon is a Harsh Mistress also make an appearance.
Mike also has a cameo in To Sail Beyond the Sunset, but I wouldn't read it just for him, as not much of his personality comes through.
After finally reading MIAHM - about a year after I planned to - I have to say that I found it to be a right little page-turner. I was engrossed from beginning to end. I read this back in November, but I plan to revisit it when I can pick up a new copy (the one I read was borrowed), and will be back with more thoughts then.
In the meantime, on the subject of his writing style in this, and the dialogue in particular, I found Manny to be really interesting - as his speech patterns reflected not only a multi-cultural Luna, but also his profession. Working with computers that are programmed by voice led him to adopt an odd syntax in his everyday speech. It is little touches like this that make Heinlein really work for me. Can't wait to read it again.