Inspections are iffy. Sometimes when you go in they'll tell you it needs to be inspected and won't hear you when you tell them it doesn't. Sometimes they don't even say the word "inspection." I found a thing online that says that motorized bicycles don't need to be inspected, and I've been telling people to print that out when they go in, because that seems like it would help convince them.
Anything over 50cc's is a no-go, unless you want to lie about it. Usually Kansas requires a title if you want to register anything, including a moped or scooter. The loophole is that Missouri doesn't title/register anything under 50cc's, so they can't make us bring in a title if it came from a state that doesn't title them. However, Missouri does register/title 150cc scooters, right? If so, the loophole doesn't apply. If you lie about it and "sell" it to us as something 50cc, you won't be able to re-register it in Missouri because the Kansas title will say it's a motorized bicycle. Or well.... in Kansas, you're allowed to have anything up to 135cc's registered as a moped so long as it doesn't exceed 30mph. Lots of people register 125cc scooters as mopeds though, even though they definitely go over 30. If we lie about the displacement (125cc instead of 150) on the form/when we're talking to the people at the treasurer's office and get it registered as a moped, then when you go back to Missouri, it WILL legally be a motorcycle under Missouri law, and you might be able to register it as such. That seems like a lot of headache, though.