Although not directly relevant to your Star Craft II question, see this similar question regarding the Diablo III client:
What are the precise differences between "playable" and "optimal"?
Blizzard uses similar technologies that support "Playable" gameplay across their different games (Diablo, StarCraft, and World of Warcraft); at least conceptually, the answer would be the same for all of those games.
As far as was what exact content is missing, incomplete, or otherwise unplayable, that would depend on the nature of the update and what content Blizzard deemed superfluous with respect to "core content" (content not required to be installed before the game is considered "Playable"). I can't say that I've ever played a Blizzard game in "Playable mode" and encountered an issue that I could directly attribute to an incomplete install or patch.
Blizzard isn't too specific on what exactly a "hiccup" is either:
Please keep in mind that if the progress bar isn’t full when you begin playing, then that means that the patch hasn't been fully applied and there may be some gameplay hiccups. That’s normal, and you can wait for the progress bar to fill completely if you’re concerned about performance...