To transfer to UW is actually much easier than getting accepted. I reluctantly admit my oldest son went to MU for 1+ years and transferred to UW. If my son had attended UWM he would have been accepted one semester earlier. All said and done the 2+ years at UW a better investment.
Indeed, I had friends who spent their freshman years at MU and UWM after getting rejected from UW and were admitted as transfers. I did the flip and went from UW to MU. I did have a couple close friends in my graduating class with high GPAs and ACT scores get rejected and waitlisted (the waitlisted one was a 3.7 GPA and 26 ACT), which was upsetting when I got to school and found they take many out of state students with much less impressive credentials-UW at that time had the lowest percentage of in state students of any public school in the country and it was quite obvious if you spent time on campus. It was also almost like "culture shock" in Madison with how they catered to out of state students. Not sure if it's still that way, but most likely.
As for the main topic at hand, MU has been perceived very well by those I've encountered after graduation in time spent living up and down the east coast. No Ivy League, but certainly not "second rate". Wouldn't even say most people think all Big Ten schools are a notch above MU-they like their #1 state schools whether they're Big Ten or ACC or SEC, and MU has been considered a strong academic school and basketball school (possibly helping the perception of the former). Even had someone ask me if MU struggles to get good basketball recruits...I was about to start with the climate when they continued the question with "because of their academic admissions standards".
When I went to school at MU in the early 2000s the girls were supremely terrible.
And yes, having lived in several places with many college campuses nearby after graduating, it only confirmed what we always thought of the girls at MU. Though they seemed to have gotten better the past couple times I had visited campus.