Your comments

Sure, I can certainly see having the thicker scrollbars as the default. I'd be ok with that, as long as it's easy for me to switch to thin or none :) So, maybe there are 3 scrollbar settings: "default", "thin", "none".

Yep, I like the idea of using the fade effect for the top/bottom of the minimap. Repeating the visual metaphor is a good thing!

The only potential problem I see with it is that it wouldn't provide a clickable affordance for scrolling the minimap. That would not bother me, personally, because I would never use such an affordance--I'm a mousewheel (magic mouse, actually) kind of guy! So, I'd be happy with the fade, although there may be some users who would not be. Maybe that should be a pref as well ... minimap_scroll_hints: "default" (none?), "arrows", "fade" or somesuch.
Both are good points! However, I think there is a relatively simple solution to the first one, and it's possible that the second is less of an issue for developers (i.e. the people most likely to be using Sublime).

When the minimap has too many lines, some sort of visual affordance (not a scrollbar on the minimap!) could be used to indicate that there is more to see either up or down. As a simple example, the minimap could have small arrows overlayed at the top and/or bottom when there is more too see. Users could use the mousewheel, or click the arrows to scroll the minimap.

As for clicking the scrollbar, I actually feel that's not something people do very often. My guess is that most users will navigate a file via keyboard, or mousewheel. I also feel that clicking on the minimap is much more useful, since you can see where it will take you before you click--whereas clicking a scrollbar is more like guessing. Of course, the thin scrollbar could still be clickable, it would just be slightly harder to target (as you pointed out). Now that I think about it, I could probably do without scrollbars entirely when the minimap is shown.

There would obviously be a problem with thin scrollbars for users who don't use the minimap, and who are inclined to click the scrollbar to navigate. In that case, maybe thicker scrollbars could be a user-configurable option?
I just realized that an even better option, when the minimap is displayed, is to forego scrollbars altogether since the minimap conveys the same information (and more!). So I'll vote for NO scrollbars when minimap shown, and thin scrollbars when minimap not shown.