The problem with javascript is not the language itself - it's a perfectly good prototyped and dynamic language. If you come from an OO background there's a bit of a learning curve, but it's not the language's fault.
Most people assume that Javascript is like Java because it has similar syntax and a similar name, but actually it's a lot more like lisp. It's actually pretty well suited to DOM manipulation.
The real problem is that it's compiled by the browser, and that means it works in a very different way depending on the client.
Not only is the actual DOM different depending on the browser, but there's a massive difference in performance and layout.
Edit following clarification in question
Suppose multiple interpreted languages were supported - you still have the same problems. The various browsers would still be buggy and have different DOMs.
In addition you would have to have an interpreter built into the browser or somehow installed as a plug in (that you could check for before you served up the page) for each language. It took ages to get Javascript consistent.
You can't use compiled languages in the same way - then you're introducing an executable that can't easily be scrutinised for what it does. Lots of users would choose not to let it run.
OK, so what about some sort of sandbox for the compiled code? Sounds like Java Applets to me. Or ActionScript in Flash. Or C# in Silverlight.
What about some kind of IL standard? That has more potential. Develop in whatever language you want and then compile it to IL, which the browser then JITs.
Except, Javascript is kind of already that IL - just look at GWT. It lets you write programs in Java, but distribute them as HTML and JS.
Edit following further clarification in question
Javascript isn't, or rather wasn't, the only language supported by browsers: back in the Internet Explorer dark ages you could choose between Javascript or VBScript to run in IE. Technically IE didn't even run Javascript - it ran JScript (mainly to avoid having to pay Sun for the word java, Oracle still own the name Javascript).
The problem was that VBScript was proprietary to Microsoft, but also that it just wasn't very good. While Javascript was adding functionality and getting top rate debugging tools in other browsers (like FireBug) VBScript remained IE-only and pretty much un-debuggable (dev tools in IE4/5/6 were none existent). Meanwhile VBScript also expanded to become a pretty powerful scripting tool in the OS, but none of those features were available in the browser (and when they were they became massive security holes).
There are still some corporate internal applications out there that use VBScript (and some rely on those security holes), and they're still running IE7 (they only stopped IE6 because MS finally killed it off).
Getting Javascript to it's current state has been a nightmare and has taken 20 years. It still doesn't have consistent support, with language features (specified in 1999) still missing from some browsers and lots of shims being required.
Adding an alternate language for interpreting in browsers faces two major problems:
Getting all the browser vendors to implement the new language standard - something they still haven't managed for Javascript in 20 years.
A second language potentially dilutes the support you already have, allowing (for instance) IE to have second rate Javascript support but great VBScript (again). I really don't want to be writing code in different languages for different browsers.
It should be noted that Javascript isn't 'finished' - it's still evolving to become better in new browsers. The latest version is years ahead of of the browsers' implementations and they're working on the next one.