I program both C# and JS on an almost daily basis and am pretty well versed in both. I have to say that JS is great for adding scripting to pages but for large apps it's a nightmare (especially when coupled w/ the dom).
I'd call something with more than 100k LOC a large app. It can get messy even before then though. The main concerns I have with Javascript are:
1) Most frameworks try to make JS into a typical OOP language which tends to hurt performance and can make debugging a PITA.
2) In "one page apps" it can become difficult to map nodes to JS objects so things get cleaned up properly. You often see memory build ups even in jQuery because of html node wrappers and events that get cached but don't get cleaned up.
3) Static analysis. It's possible to get some level of static analysis if you use JSDoc but it's still very poor compared to something like C#. For example, you need to add tons of JSDoc code to make autocomplete somewhat usable. After using something like Resharper, you can really see how lack of good static analysis hurts.
4) Difficult to refactor large apps. Since the static analysis is poor, it's difficult to use tools to create dependency graphs, finding usages, etc... I really wish Js would just let you specify a type of an object like ActionScript 3 does. You can still use var if you want but 99% of the time an object has an expected type.
5) Lack of visibility keywords. This makes it hard to organize code into modules and prevent programmers from getting access to things they aren't supposed to. I'm sure there are entire debates on this point alone.
6) Performance. The browsers try to do tons of optimizations during runtime to speed up javascript. If you want to get the most out of JS, you really need to know about them (e.g. always initialize your class vars in the same order).