In the Yale short take asking about what you admire most in others, I wrote "the lack of need of approval from others." It should be "lack of need FOR approval from others." Is this a glaring mistake/should I be worried? And while it may seem like that was a careless mistake, I read that phrase over at least 10 times and saw nothing wrong with it...I proofread each part of my application 3+ times before sending it out. Hopefully you can give me some peace of mind.
Eh, I'm in the same boat. I could kick myself, but I really do trust the admissions process. If they want to admit you, they're not going to reject you because of that mistake. Your typo is pretty mundane (matter of syntax, not of grammar), but even if it were glaring -- there's nothing to be done!
Don't worry about that mistake. It won't come across as careless, because it's really simple. Errors related to things like phrasal verbs or noun-preposition agreement are easy to overlook (for example, some people say "qualms with" rather than the correct "qualms about," just as you said "need of" instead of "need for"). No big deal - don't sweat it.
Errors that really stand out are the ones that should cause you the most worry. For instance, confusing words like "your" or "you're" would look pretty horrible. Similarly, errors in syntax are also very bad, because they're extremely obvious. You don't even need to look for syntax errors in order for them to stand out. Mistakes in syntax are typically uncommon to those fluent in English, however.
^ I only just realized that your username is "vicariousparent." Since I first saw your username a few months ago, I thought it said "viciousparent." You now seem significantly more pleasant than you originally did.
And this post is the reason why I refuse to read back any of my application answers once I've submitted it. I just know I'm going to discover that I've accidentally slipped a your/you're mistake in there or that a rogue "LOL" has worked its way into the essay. I shudder just thinking about it.