Is there a way to limit the number of blocks a user can insert into a block container? The design is only for 3 items, so I don't want my client to be adding more than that.
Not sure if you can limit it directly in the UI, but you can limit it when saving the page. See this article: http://world.episerver.com/code/dannymurphy/contentarea-item-limiting/
Another option could be to create your own ContentAreaRenderer and do your magic there. I wrote a blog article about manipulating a single item but I think you could change how all items are rendered. http://www.kloojed.com/render-contentarea-items-with-ehm-spacing/
Have a look at Henriks blog post for an example of how to implement custom validation to do that:
Thank you, Paul - Henrik's solution works well enough for my purposes. I appreciate your help!