If there's anything wrong with MSG that isn't simply due to sodium intake, I think it's unknown to science (at least in the sense that there's no theory about it with any wide uptake). MSG is also intensively studied and has a very similar mechanistic story to aspartame.
One thing that is "wrong" with MSG is that a lot of restaurants overuse it as a condiment. So you're paying money for a good food experience, but you're getting the taste equivalent of instant ramen noodles.
I actually _like_ instant ramen noodles and MSG, and I use MSG when cooking. But it feels like cheating when fancy restaurants also use it.