Two things that I find ( in my opinion ) unpleasant :
1. Source code is hard to read ( some strange indentation and a lot of empty lines )
2. Support for dynamic content will do a lot of repaints.
Most good OpenType fonts have kerning data built in, and its pretty simple to enable this feature for most modern browsers (Safari is lagging, see font-feature-settings). There certainly are times when you want to override the default kerning, but its few and far between, and certainly not a good idea for body copy.
I'd rather have improper kerning for old browsers, and nice kerning for new browsers than trust designers to properly manually adjust the kerning themselves.
You've got it backwards. Never trust a font to provide your kerning, always adjust. Proper kerning is a fundamental tenant of good typography. Designers have always and will always manually adjust kerning.
Yes there are times, especially with display type, that you want to adjust the kerning between a few pairs of glyphs, but to say to "never trust a font to provide your kerning" suggests to me that you use a lot of poorly designed free fonts rather than professionally realized typefaces from reputable font foundries.
I would love it if the browsers would all support the built in kerning in a font by default, with a way to override it manually.
If you are using quality fonts, as you should be, you will only need to adjust the kerning in very rare cases. The type designers are the ones who have to concern themselves heavily with the font kerning. Which is why font design software, such as fontlab or glyphs, have an insane amount of kerning related functionality, whereas the kerning provided by something like, say, photoshop or indesign, will do what you need it to--which is make minimal adjustments in corner cases.