Probably the best example I have of learning a feature by accident is macro recording. Occasionally I used to hit the q key when I was meaning to hit w to navigate by word. After a few months of wondering what "recording" meant, I looked it up and it has become one of the most important components of my workflow ever since.
However, I would argue that for the vast majority of Vim features, learning "by accident" is unfeasible. Many commands give no visual or verbal indication of what happened (consider marks). Further, both the tutorial and the Vim wiki are very readable and can cover a lot more ground than by hoping to accidentally hit a goldmine feature while mashing random key combinations.
I'd argue that the best way to learn anything in vim is to read the docs. When I first started with vim, I was just jumping in, trying to figure it out as I go. All that really yielded was frustration. Though I guess that frustration is what led me to actually read the help, so in a roundabout way, maybe I agree!
The vim docs are surprisingly great. With many ancient open-source tools I usually find better explanatory docs elsewhere on the web, so I used to spend time reading tips and things online for vim. Once you know the basics though, the vim docs are way better than anything else I've seen written about the editor.
I love vim more than almost any other software. But it really is not very discoverable 'by accident.' You have to read documentation and grok the system or you don't get much benefit.
Especially at the beginning, when you do something like starting to type words while in normal mode and the screen scrolls and a bunch of crap gets deleted, there isn't any highly visible way to see what happened and it's easy to get discouraged.
Accidents like that might provide motivation to find the correct way, but rarely much information on what to do.
Vim is excellent software and usable (as in easy to actually use, once you are at cruising altitude) but easily discoverable it is not (until you grasp the system's fundamentals, then you don't need to 'discover' much - you just express what you mean to do without needing to memorize 40,000 hand-contorting ctrl-alt-chords, or configure your text editor in LISP)
Also helpful is comparing vimrc files. Here are some things I put in mine:
color slate
set tabstop=4
set shiftwidth=4
set expandtab
set autoindent
set mouse=a
set laststatus=2
autocmd FileType make set noexpandtab
set tags=tags;/
However, I would argue that for the vast majority of Vim features, learning "by accident" is unfeasible. Many commands give no visual or verbal indication of what happened (consider marks). Further, both the tutorial and the Vim wiki are very readable and can cover a lot more ground than by hoping to accidentally hit a goldmine feature while mashing random key combinations.