Not if the browsers implement it (which seems the best solution)

sounds awful. So now you're putting a checkbox next to any password field?

Designers have to be aware that in some browsers there'll be a checkbox next to password fields.

checkbox? if the broswer implements it you dont need a checkbox (icon in the field, menu option, context menu option - plenty of neater ways to implement it than a checkbox)

How a tiny button inside the password field like the "Browse" or "Choose file" in file upload field?

That button isn't tiny, and is in fact very obtrusive. It makes creating designs and layouts hard enough as it is, and the file dialog isn't even used very often.

I'm pretty sure you can implement something like this on the web with some simple javascript, dynamically changing the input type from "text" to "password" and vice versa.

I mean, tiny button. Not a huge button that is used by file upload field. Something like this: http://i30.tinypic.com/34f0knt.png

Or you can put this option in menu or status bar or whatever.

By the way, I don't understand your complaints about design and layouts. I've never had problems with designing forms. Maybe this is because I didn't try to replace native controls with some uber-fancy things? (which is a good thing)

...thereby breaking the semantics of the password input type. If it's going to be changed by Javascript, it should be a CSS style called "masked" or something.