My company uses their own typeface for a UI, and it's... not great.

The most obvious issue is the kerning. I've never edited a typeface in my life; is it worth trying, or is this best left to the experts? Is kerning-only a reasonable newbie project?

Is it a free/open source typeface or a commercial one? For the latter changes are usually not allowed and you would have to contact the foundry about it. 

I'm not sure.

My idea is to fix the kerning a little and then demo the improvement, motivating a more professional review.

In any case my question remains.

Well, if you want to start with just a demo, go for it. (If the license allows it)

What is required technically depends on the font itself. If its a Latin 1 font with simple kerning pairs, the technical process of editing and adding pairs isn’t that complicated. It’s all about the design decisions. 

If its a more complex font with many characters and OpenType class-kerning, the learning curve is steeper. 

Thanks - that helps orient me to the challenge!